Question

a jogger runs 4 miles per hour faster downhill than uphill. if the jogger can run 5 miles downhill in the same time that it takes to run 3 miles uphill, find the rate in each direction

Answer 1

Answer: the rate uphill is 6 mph.

The rate downhill is 10 mph

Step-by-step explanation:

Let x represent the rate at which the jogger ran uphill.

The jogger runs 4 miles per hour faster downhill than uphill. This means that speed at which the jogger ran downhill is (x + 4) mph

Time = distance/speed

if the jogger can runs 5 miles downhill, then the time taken to run downhill is

5/(x + 4)

At the same time, the jogger runs 3 miles uphill. It means that the time taken to run uphill is

3/x

Since the time is the same, it means that

5/(x + 4) = 3/x

Cross multiplying, it becomes

5 × x = 3(x + 4)

5x = 3x + 12

5x - 3x = 12

2x = 12

x = 12/2

x = 6

The rate downhill is 6 + 4 = 10 mph

Answer 2

Answer:

Downhill: 10 miles/hour

Uphill: 6 miles/hour

Step-by-step explanation:

(5/t) - (3/t) = 4

2/t = 4

t = ½

Downhill: 5/½ = 10 miles/hour

Uphill: 3/½ = 6 miles/hour