QuestionAmy drove 737 miles in 11 hours. At the same rate, how long would it take her to drive 871 miles?

Studdy Solution

STEP 1

1. Amy drove 737 miles in 11 hours.
2. We are asked to find the time it would take her to drive 871 miles at the same rate.

STEP 2

1. Calculate Amy's driving rate in miles per hour.
2. Set up a proportion to find the time for 871 miles.
3. Solve the proportion for the unknown time.

STEP 3

Calculate Amy's driving rate in miles per hour.
Amy's rate = $\frac{\text{Total miles driven}}{\text{Total hours}} = \frac{737 \text{ miles}}{11 \text{ hours}}$
Calculate the rate:
$\text{Rate} = \frac{737}{11} \approx 67 \text{ miles per hour}$

STEP 4

Set up a proportion to find the time for 871 miles.
Let $t$ be the time in hours to drive 871 miles.
$\frac{737 \text{ miles}}{11 \text{ hours}} = \frac{871 \text{ miles}}{t \text{ hours}}$

STEP 5

Solve the proportion for the unknown time $t$ .
Cross-multiply to solve for $t$ :
$737t = 871 \times 11$
Calculate $871 \times 11$ :
$871 \times 11 = 9581$
Now solve for $t$ :
$737t = 9581$
Divide both sides by 737:
$t = \frac{9581}{737}$
Calculate the division:
$t \approx 13$
So, it would take Amy approximately 13 hours to drive 871 miles.

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