Question

Ben starts walking along a path at 3 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 7 mi/h. How long (in hours) will it be before Amanda catches up to Ben?

Enter the exact answer.
Hint: The distance formula is that distance = rate * time, so for example in one and a half hours, Ben has walked 3 * 1.5 miles.

Answer 1

Explanation:

Distance = speed * time

For Ben:

speed = 3mi/hr

Time = (x+1.5)hr

Distance = 3 * (x+1.5)

Distance = 3(x+1.5)

For Amanda:

Speed = 7mi/hr

time = 1x

Distance = 7x

Since they cover the same distance then:

3(x+1.5) = 7x

3x + 4.5= 7x

3x-7x = -4.5

-4x =-4.5

x = 4.5/4

x = 1.125 hr

The time taken by Amanda is 1.125 hr