It’s the end of the semester, and sisters Sarah and Chelsea are eager to head home for the summer. It’s a long drive, and Sarah’s old car can manage an average speed of only 55 miles per hour, so she leaves early in the morning. An hour later, Chelsea follows her at an average speed of 75 miles per hour. How many hours will it take Chelsea to catch up to Sarah?

Question

It’s the end of the semester, and sisters Sarah and Chelsea are eager to head home for the summer.  It’s a long drive, and Sarah’s old car can manage an average speed of only 55 miles per hour, so she leaves early in the morning.  An hour later, Chelsea follows her at an average speed of 75 miles per hour.  How many hours will it take Chelsea to catch up to Sarah?

Reiny · Answer

let the time passed since Chelsea left be t hrs

So Chelsea went for t hrs
Sarah went for t+1 hrs

When they meet, they both have covered the same distance, so

75t = 55(t+1)
75t = 55t + 55
20t = 55
t = 55/20 or 2.75 hrs

Chelsea went for 2.75 hrs of 2 hrs and 45 minutes
Sarah went for 3.75 hrs or 3 hours and 45 minutes

State your conclusion