Sheila leaves on a long trip driving at a steady rate of 25 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 50 miles per hour. How long after Sheila leaves home will Allison catch up?
Distance = rate x time
Sheila's rate = 25 mph
Sheila's time = t
Sheila's distance = 25t {distance = rate x time}
Allison's rate = 50mph
Allison's time = t - 2 {she started 2 hours later or lost two hours off of the starting time}
Allison's distance = 50(t - 2) = 50t - 100 {distance = rate x time}
25t = 50(t - 2) {when Allison catches up with Sheila the distances are equal}
25t = 50t - 100 {used distributive property}
-25t = -100 {subtracted 50t from each side}
t = 4 {divided each side by -25}
{t corresponds with Sheila's time, which is what the question is asking for}
In 4 hours after Sheila leaves Allison will catch up with Sheila
- Algebra House
