Question

Sally spent 6 hours walking from her house to the lake and back. She walked to the lake at a rate of 4mph and walked back at a rate of 2mph. What is the distance for her house to the lake?

Answer 1

Speed = Distance / time

v = s / t

In this case s = the distance for her house to the lake.

v1 = s / t1

She walked to the lake at a rate of 4 mph so:

v1 = s / t1

4 = s / t1

Multiply both sides by t1

4 t1 = s

Divide both sides by 4

t1 = s / 4

She walked back at a rate of 2mph so:

v2 = s / t2

2 = s / t2

Multiply both sides by t2

2 t2 = s

Divide both sides by 2

t2 = s / 2

Sally spent 6 hours walking from her house to the lake and back mean:

t1 + t2 = 6


s / 4 + s / 2 = 6

s / 4 + 2 s / 4 = 6

3 s / 4 = 6

Multiply both sides by 4

3 s = 24

Divide both sides by 3

s = 8

The distance for her house to the lake = 8 miles

Proof:

v1 = s / t1

t1 = s / v1

t1 = 8 / 4

t1 = 2 h


v2 = s / t2

t2 = s / v2

t2 = 8 / 2

t2 = 4 h


t1 + t2 = 2 h + 4 h = 6 h