Answer:
2 hours and 3 hours
Explanation:
First, convert the time from hours and minutes to just hours.
1 hr and 12 min = 1.2 hr
Let's say t is the time it takes for one mail carrier, and t+1 is the time for the other mail carrier.
The speed of the first mail carrier is 1 route / t hours.
The speed of the second mail carrier is 1 route / (t+1) hours.
Their combined speed is:
1 route / 1.2 hours = 1 route / t hours + 1 route / (t+1) hours
Solving this equation:
1 / 1.2 = 1 / t + 1 / (t + 1)
5 / 6 = 1 / t + 1 / (t + 1)
Multiply both sides by 6t (t + 1):
5t (t + 1) = 6 (t + 1) + 6t
5t² + 5t = 6t + 6 + 6t
5t² + 5t = 12t + 6
5t² − 7t − 6 = 0
Factor:
(t − 2) (5t + 3) = 0
t = 2 or -0.6
Since t must be positive, t = 2, so t+1 = 3.
It takes each carrier 2 hours and 3 hours working alone.
The answer key must have a mistake. If one of the carriers can deliver mail in 1 hour, then it would take less than 1 hour working together.