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?
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
To find out how many hours it will take Chelsea to catch up to Sarah, we can set up a distance equation.
Let's assume that Chelsea catches up to Sarah after 't' hours.
In this time, Sarah will have driven a distance of 55t miles (since her average speed is 55 miles per hour).
On the other hand, Chelsea will have driven a distance of 75(t-1) miles since she started one hour later than Sarah.
Since Chelsea catches up to Sarah, their distances covered will be equal:
55t = 75(t-1)
Let's solve this equation to find the value of 't'.
55t = 75t - 75
-20t = -75
Dividing both sides of the equation by -20, we get:
t = 3.75
Therefore, it will take Chelsea 3.75 hours to catch up to Sarah.