Distance, Rate, Time Problem

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?

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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

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