Question

Shelia leaves on a long trip driving at a steady rate of 45 miles per hour. Her sister Allison leaves from the same location traveling to the same destination 2 hours later. She drives at a steady rate of 60 miles per hour. How long after Shelia leaves home will Allison catch up?

Answer 1

Let the time Shelia spend on the road be t. Thus, the time Allison spends on the road will be t-2 (assuming t is at least 2 hours).

Since distance is speed*time, we want the time when the distance Allison and Shelia to be the same:
$45*t=60*(t-2)$
$120=15t$
$t=8$

Therefore, Allison will catch up the Shelia after Shelia is on the road for 8 hours (6 hours driving time for Allison).

Answer 2

Set an equation:

Let x=hours

60x=45x+90       Subtract 45x from both sides

15x=90           Divide both sides by 15

x=6

Answer: It will take Alison 6 hours to catch up to Shelia.