Question

A bus station runs a shuttle service to and from the airport. A shuttle that left the station traveling at 39 miles per hour is passed by a second shuttle that left 30 minutes later traveling at a rate of 42 miles per hour. How far did the first shuttle travel before it was passed by the second shuttle?

Answer 1

To find the distance that the first shuttle traveled before it was passed by the second shuttle, we need to use the formula d = rt, where d is the distance traveled, r is the speed at which the shuttle is traveling, and t is the time elapsed. We can use this formula to find the distance traveled by each shuttle and then subtract the distance traveled by the first shuttle from the distance traveled by the second shuttle to find the distance the first shuttle traveled before it was passed.

For the first shuttle, the speed is 39 miles per hour and the time elapsed is 30 minutes. Since there are 60 minutes in an hour, the time elapsed in hours is 30 minutes / 60 minutes/hour = 0.5 hours. So, the distance traveled by the first shuttle is 39 miles/hour * 0.5 hours = 19.5 miles.

For the second shuttle, the speed is 42 miles per hour and the time elapsed is 30 minutes. Since there are 60 minutes in an hour, the time elapsed in hours is 30 minutes / 60 minutes/hour = 0.5 hours. So, the distance traveled by the second shuttle is 42 miles/hour * 0.5 hours = 21 miles.

Therefore, the distance that the first shuttle traveled before it was passed by the second shuttle is 21 miles - 19.5 miles = 1.5 miles.