Question

Ben starts walking along a path at 2 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?

Answer 1

Answer:

Amanda will catch up Ben after 0.6 hours.

Step-by-step explanation:

Amanda begins jogging along the same path at 7 mi/h.

This means that Amanda's position, after t hours, is given by:

$A(t) = 7t$

Ben starts walking along a path at 2 mi/h.

Amanda leaves after one and a half hour, which means that Ben will be at position 2*1.5 = 3. So Ben's position after t hours is given by:

$B(t) = 3 + 2t$

How long (in hours) will it be before Amanda catches up to Ben?

This will happen when:

$A(t) = B(t)$

So

$7t = 3 + 2t$

$5t = 3$

$t = \frac{3}{5}$

$t = 0.6$

Amanda will catch up Ben after 0.6 hours.