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?
d1 = Sarah's distance
d2 = Chelsea's distance.
d2 = d1 + 55
Vc*T = Vs*T + 55
75T = 55T + 55
20T = 55
T = 2.75 h. = 2h-45 Min.
To determine how many hours it will take Chelsea to catch up to Sarah, we need to find the time it takes for them to cover the same distance.
Let's assume it takes Chelsea "t" hours to catch up to Sarah.
In the first hour, Sarah's car travels 55 miles (since she has a constant speed of 55 mph and she leaves an hour earlier).
For Chelsea to catch up to Sarah, she needs to cover this initial distance of 55 miles, as well as the distance Sarah has traveled in "t" hours.
Since Chelsea's average speed is 75 mph, and she travels for "t" hours, Chelsea covers a distance of 75t miles.
So, for Chelsea to catch up to Sarah, she needs to cover a total distance of 55 + 75t miles.
Since Sarah and Chelsea are traveling at different speeds, we can equate their respective distances to find the time it takes for Chelsea to catch up:
Distance covered by Sarah = Distance covered by Chelsea
55 + 55t = 75t
Now we can solve for "t":
55t = 75t - 55
55t - 75t = -55
-20t = -55
t = (-55)/(-20)
t = 2.75
Therefore, it will take Chelsea approximately 2.75 hours to catch up to Sarah.