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 5 mi/h. How long (in hours) will it be before Amanda catches up to Ben?

It would take Amanda 2.25 hours to catch up with Ben

Speed is the ratio of distance to time. It is given by:

Speed = distance/time

Given that Ben covers a distance d at time t, hence:

3 = d/t

d = 3t

Since Amanda leaves One and a half hours (1.5) after Ben leaves, hence Time = t - 1.5

5 = d/(t - 1.5)

d = 5t - 7.5

Since they catch up, hence:

3t = 5t - 7.5

2t = 7.5

t = 3.75 hours

Time for Amanda = t - 1.5 = 3.75 - 1.5 = 2.25 hours

Hence it would take Amanda 2.25 hours to catch up with Ben.

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2 hours 15 minutes

Step-by-step explanation:

Given that :

Ben's speed = 3 mi/hr

One and half hours after Ben leaves = 1.5 hours

Ben's distance = 3 mi/hr * 1.5 = 4.5 miles

Amanda's speed = 5 mi/hr

Time taken before Amanda catches up:

Let time taken = x

Distance = speed * time

Ben's distance = Amanda's distance

4.5 mi + (3 * x) = 5 * x

4.5 + 3x = 5x

4.5 = 5x - 3x

4.5 = 2x

x = 4.5 / 2

x = 2.25 hours

Time taken = 2.25 * 60 = 135 minutes = 2 hours 15 minutes

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step-by-step explanation: