Question

Phoebe spends 1.7 hours training for an upcoming race. She runs full speed at 3.7 miles per hour for the race distance; then she walks back to her starting point at 2.4 miles per hour. How long does she spend running?

Round your answer to 2 decimal places.

Answer 1

Step-by-step explanation:

Rate • Time = Distance

Let tr = time she ran

Let tw = time she walked

RUNNING THE RACE:

Rate • Time = Distance

8 tr = Distance

WALKING THE RACE:

Rate • Time = Distance

2 tw = Distance

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The distance for each leg is the same (ran the distance, walked the return distance)

8tr = 2tw (Equation 1)

The total time was 2 hours

tr + tw = 2 (Equation 2)

Solving Equation 2 for tr, tr = 2 - tw

Substituting 2-t for tr in equation 1, then solving for tw

8(2 - tw) = 2tw

16 - 8tw = 2tw

16 = 2tw + 8tw

16 = 10tw

10tw = 16

tw = 16/10

tw = 1.6

She walked for 1.6 hours ... 1 hour, 36 minutes

She ran for 2 - 1.6 hours = .4 hours = 24 minutes

Answer 2

Answer:

2.47 miles

Step-by-step explanation:

Let distance Phoebe ran is "d".

d = ts (distance = time × speed) ⇒ t = $\frac{d}{s}$

$\frac{d}{3.7}$ + $\frac{d}{2.4}$ = 1.7

$\frac{2.4d+3.7d}{3.7*2.4}$ = 1.7

6.1d = 1.7 × 3.7 × 2.4

d = $\frac{15.096}{6.1}$

d ≈ 2.47 miles