A backpacking stove is fueled by a canister that initially contains grams of propane. While cooking, the stove consumes propane at a constant rate of grams every minutes. If the canister now contains grams of propane, for how many minutes has the stove been running?

Solution available with step-by-step explanation

SAT Linear Equations in One Variable Question 20 | Free SAT Prep | Aniko

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Question 20·Medium·Linear Equations in One Variable

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A backpacking stove is fueled by a canister that initially contains $250$ grams of propane. While cooking, the stove consumes propane at a constant rate of $4$ grams every $3$ minutes. If the canister now contains $174$ grams of propane, for how many minutes has the stove been running?

For rate problems like this, first find the change in the quantity (here, grams used) by subtracting final from initial. Then use either a proportion or the formula (time) = (amount used) ÷ (rate) while keeping units straight (grams with grams, minutes with minutes). When the rate is given as "X units every Y minutes," it is often fastest to think in terms of "blocks" (X units per Y minutes), count how many blocks occurred, and then multiply by the minutes per block to get the total time.

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Start with how much propane was used

Compare the initial amount (250 grams) with the current amount (174 grams). What operation will tell you how many grams have been used?

Use the rate to find how many usage intervals occurred

The stove uses 4 grams every 3 minutes. Once you know how many grams were used, divide by 4 to find how many 3‑minute intervals passed.

Convert intervals into minutes

Each interval is 3 minutes long. After you know how many intervals there were, what should you do with that number to get total minutes?

Desmos Guide

Compute total running time in one expression

In Desmos, type the expression (250 - 174) / (4/3) and press Enter. The value Desmos gives is the total number of minutes the stove has been running.

Step-by-step Explanation

Find how many grams of propane were used

The canister started with $250$ grams and now has $174$ grams.

Calculate how many grams were used:

$250 - 174 = 76$ grams of propane have been consumed.

Relate grams used to the consumption rate

The stove uses $4$ grams every $3$ minutes.

So each "usage block" is:

$4$ grams of propane
over $3$ minutes of time

To find how many such $4$ -gram blocks were used, divide total grams used by $4$ :

$76 \div 4 = 19$

So the stove has gone through $19$ blocks of $4$ grams.

Convert number of blocks to minutes

Each block of $4$ grams corresponds to $3$ minutes of stove use.

So total time is:

$19$ blocks $\times$ $3$ minutes per block $= 19 \times 3$ minutes.

Now multiply to get the total minutes.

Compute the total running time

Multiply $19 \times 3$ :

$19 \times 3 = 57$ .

So the stove has been running for 57 minutes.

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation