A Tank Holds 48.6 Gallons of Water. Water Drains Out at 2.9 Gallons per Minute for 9.75 Minutes. Which Is the Best Estimate of the Amount of Water Left in the Tank: About 20 Gallons

The best estimate is about 20 gallons left. The exact arithmetic gives 48.6 − (2.9 × 9.75) = 48.6 − 28.275 = 20.325 gallons. Because the question says "estimate," the expected answer is the rounded figure near 20, so 20.3 gallons is the precise value and 20 gallons is the estimate.

The gap between those two numbers matters more than it first appears. This question is built to test whether you estimate before you calculate, and the distractors are designed around the mistakes students make when they do it the other way around. Below is the full breakdown: the exact product, the rounding logic, the answer choices you're likely to see, and the traps that produce the wrong one.

The Exact Subtraction Behind the Estimate

Run the multiplication first and the subtraction second, and keep every decimal until the end. 2.9 gallons per minute times 9.75 minutes equals 28.275 gallons drained. Subtract that from the starting 48.6 gallons and you get 20.325 gallons remaining. That is the exact answer to the arithmetic as written.

Rounding at this stage is optional, because 20.325 is already a clean terminating decimal. Note what the units do: gallons per minute multiplied by minutes cancels the time unit and leaves gallons, which is why the product can be subtracted directly from the tank's capacity. No conversion step is needed.

The subtraction itself is worth checking once by hand. 48.600 minus 28.275 aligns the decimal points and gives 20.325. If you get 20.325 but your neighbor gets 20.375 or 19.325, the difference is almost always a borrowing slip in the hundredths column, not a conceptual error.

One habit pays off here: write the multiplication vertically. 2.9 × 9.75 has three decimal places total (one in 2.9, two in 9.75), so the product carries three: 28.275. Students who drop a decimal place get 282.75 and then subtract a number five times larger than the tank holds, which is an immediate red flag if you sanity-check against the starting volume.

Why "Best Estimate" Points to 20 Gallons, Not 20.325

The wording "best estimate" signals that the answer choices will be round numbers, and you should pick the one closest to your computed value. On a multiple-choice test, 20 gallons is the choice that sits nearest to 20.325. If 20.3 appears as an option, take it; if only whole numbers appear, take 20.

Estimation also lets you skip the long multiplication entirely. Round 2.9 up to 3 and 9.75 up to 10, and you get 30 gallons drained from roughly 49 gallons, leaving about 19. That rough pass lands within about 1.3 gallons of the true answer, which is close enough to eliminate any choice in the 30s or 40s.

The direction of your rounding matters if you want the estimate to stay honest. Rounding 2.9 up to 3 overstates the drain, so the rough estimate understates what's left; rounding 9.75 up to 10 does the same. Both roundings push the estimate below 20.325, which is why 19 is a defensible estimate while 22 is not.

Tests that ask for an estimate usually accept a small band around the true value. In a classroom setting, anything from about 19 to about 21 gallons reflects correct reasoning; 20 is simply the cleanest landing point. The precise 20.325 answer should still be shown in your work if the test allows it, because it proves the estimate came from real arithmetic.

Reading the Rate as a Speed, Not a Total

The most common misreading treats 2.9 gallons per minute as 2.9 gallons drained in total, which yields 48.6 − 2.9 = 45.7 gallons and misses by more than 25 gallons. A rate is a speed of flow; it only becomes a quantity when you multiply by how long the flow lasts. The phrase "per minute" is the signal that multiplication is required.

A second misreading multiplies the tank's capacity by the time. Doing 48.6 × 9.75 produces 473.85, a number larger than the tank ever held, which should immediately look wrong. Any intermediate result bigger than the starting volume is a sign the wrong quantities were combined.

Watch the time unit too. The rate is per minute and the duration is in minutes, so they match. If a problem gives the rate per minute but the duration in seconds or hours, convert first. A 9.75-minute drain is 585 seconds, and a rate of 2.9 gallons per minute is about 0.0483 gallons per second; multiplying those gives the same 28.275 gallons, which is a useful cross-check.

Keep the rate constant in mind as an assumption. The question implies a steady 2.9 gallons per minute for the entire 9.75 minutes, which is how textbook drain problems work. Real tanks slow down as they empty because pressure drops, a point covered later, but that physics is outside what this question asks.

Checking the Work With Round Numbers

A thirty-second estimation pass catches most errors before they cost you a point. Round 48.6 to 50 and 2.9 to 3, then multiply 3 by 9.75 to get 29.25 drained, leaving about 20.75. That rough answer sits within half a gallon of the exact 20.325, which confirms the computation is in the right neighborhood.

Try a second pass with different roundings to see how stable the estimate is. Round 48.6 down to 48 and 2.9 up to 3: 3 × 9.75 = 29.25, and 48 − 29.25 = 18.75. Round 48.6 up to 49 and 2.9 down to 2.5: 2.5 × 9.75 = 24.375, and 49 − 24.375 = 24.625. The cluster of rough answers spans roughly 18.75 to 24.6, centering near 20.

Here is the same check laid out as a table, with each row using a different rounding strategy:

The table's lesson is that aggressive rounding of a small rate creates the biggest error. Rounding 2.9 down to 2.5 shifts the drain by nearly 4 gallons, which is why rounding the rate carefully matters more than rounding the tank size.

For a timed test, the 3 × 10 pass is the one to run. It takes about five seconds and reliably lands you within about 1.5 gallons, which is enough to pick 20 from a list of whole-number choices spaced 10 apart.

The Answer Choices You'll See and Why They Exist

Textbook versions of this problem usually offer four or five options, and each wrong option corresponds to a specific mistake. Knowing the mistake behind each number lets you spot the trap without redoing the math.

The 30-gallon distractor is the sneakiest, because estimating the drain correctly is half the work and feels like finishing. The question asks for water left, so the subtraction is mandatory. Half-finished estimates are exactly what multiple-choice designers bank on.

If you see an option in the 470s, that's the capacity-times-time error described earlier, and its presence tells you the test expects you to catch unit mismatches. Seeing it should make you confident rather than confused, since you now know where it comes from.

Where the Model Breaks Down in Real Tanks

The linear calculation assumes the flow rate stays at 2.9 gallons per minute for all 9.75 minutes, and real tanks don't behave that way. Drain rate through an opening depends on the height of water above it, so a fuller tank drains faster and a nearly empty one drains slower. Engineers model this with Torricelli's law, which relates outflow speed to the square root of the head height, credited to Evangelista Torricelli's 1643 work.

For a tenth-grade word problem, none of that applies: the constant rate is given as a fact and you're meant to use it. But knowing the assumption exists is useful, because it explains why the answer is called an estimate rather than a measurement. The phrase quietly acknowledges that the constant-rate model is an approximation of reality.

The discrepancy grows with the shape of the tank. A tall, narrow cylinder loses head height quickly as it drains, so its flow slows sharply near the end. A wide, shallow tank keeps a more stable head and tracks the linear model more closely. The problem doesn't specify a shape because the shape doesn't matter under a constant-rate assumption.

If you ever need to compute drain time for a real tank, the linear method gives a lower bound on time to empty, since the real flow slows down and takes longer. That's a practical use for the very assumption this problem asks you to accept.

A Worked Variant With a Slower Drain

Change one number and the whole feel of the problem shifts. Suppose the drain runs at 1.45 gallons per minute for 19.5 minutes. The product is identical, 28.275 gallons, because 1.45 × 19.5 = 28.275. The water left is still 20.325 gallons, and the estimate is still about 20.

That equivalence isn't a coincidence. Halving the rate and doubling the time leaves the total drained unchanged, which is the core insight of rate problems: what matters for the final volume is the product of rate and time, not either factor alone. Students who fixate on the rate miss this.

Now try a variant where the time changes instead. At 2.9 gallons per minute for 15 minutes, the drain is 43.5 gallons, leaving 5.1 gallons, which is a much tighter margin against the tank's 48.6-gallon capacity. At 2.9 gallons per minute for 16.75 minutes, the drain reaches 48.575 gallons, leaving just 0.025 gallons, essentially empty.

That last figure is worth remembering: a 48.6-gallon tank draining at 2.9 gallons per minute empties in about 16.76 minutes. The 9.75 minutes in the question is only about 58 percent of the way to empty, which is another way to confirm that a substantial amount should remain.

Tying the Numbers Back to the Ten-Second Version

The entire problem collapses to three numbers and one operation order. Multiply the rate by the time to get gallons drained, then subtract from the capacity to get gallons remaining. Everything else in this article exists to protect that sequence from the four or five ways it can go wrong.

A useful mental template for any drain problem: what's in the tank, how fast it leaves, how long it leaves for. Fill those three slots with 48.6, 2.9, and 9.75, and the arithmetic follows without decisions. The template generalizes to filling problems too, where the product gets added instead of subtracted.

For a quick final answer to carry into a quiz: the water left is 20.325 gallons, and the best estimate is 20 gallons. If your test wants a decimal, write 20.3. If it offers only whole numbers, pick the one nearest 20.

The estimate-versus-exact distinction is the last thing to keep straight. An estimate is a defensible round number; the exact value is what the arithmetic produces. Good test-takers produce both and let the answer choices decide which to report.

FAQ

Is 20.325 gallons the same answer as 20 gallons?

No, but they're close enough for an estimate. The exact value is 20.325 gallons, while 20 is the rounded estimate the question asks for. On a test with whole-number choices, 20 is the intended pick; if 20.3 appears, choose it instead. Writing 20.325 as your final answer when the question says "estimate" can cost points for over-precision.

What if the tank starts with only 25 gallons instead of 48.6?

At 25 gallons, the same drain of 28.275 gallons exceeds the starting volume, which is physically impossible for a simple tank. The math would give negative 3.275 gallons, and the correct interpretation is that the tank runs dry partway through, after about 8.6 minutes. Word problems avoid this by giving a starting volume larger than the total drain, which is why 48.6 works.

Does the tank's shape change the answer?

Under the constant-rate assumption, no. The problem gives a fixed 2.9 gallons per minute regardless of water depth, so shape never enters the calculation. In a real tank, shape affects how quickly the flow slows as the water level drops, and a tall narrow tank would deviate more from the linear model than a wide shallow one. The word problem deliberately sidesteps that physics.

How long would it take to empty the tank completely?

At 2.9 gallons per minute, a full 48.6-gallon tank empties in about 16.76 minutes, since 48.6 ÷ 2.9 = 16.759. The 9.75 minutes in the question is a little over half that time, which is another reason roughly 20 gallons should remain rather than a small puddle. The empty-time figure also gives you a fast upper bound for sanity-checking any drain problem.

Why do so many people answer 30 gallons?

They estimate the drain correctly with 3 × 10 = 30 and stop there, forgetting the subtraction. The question asks for water left in the tank, so the drained amount must come off the starting volume. Test designers include 30 as a distractor precisely because estimating the drain is the satisfying, natural half of the work.

Can I just subtract 2.9 from 48.6?

That produces 45.7 gallons, which is wrong by more than 25 gallons. Subtracting the rate treats a per-minute speed as a one-time quantity, as if the tap released 2.9 gallons in total. Rates must be multiplied by a duration before they can be subtracted from a volume, and the word "per" is the clue that multiplication is required.

What's the fastest way to estimate this on a timed test?

Round to 3 gallons per minute and 10 minutes to get 30 gallons drained, then subtract from 50 to leave about 20. The whole pass takes about five seconds and lands within about 1.3 gallons of the exact 20.325. Use it to eliminate choices, then do the precise multiplication only if two remaining options are close together.