Question

I need to know the explanation on how to find the answer to #21. On the text book answer key it states that the answer is ons carrier takes 1 Hour while the other carrier takes 2 Hours. This is an algebra question.

Answer 1

Answer:

2 hours and 3 hours

Step-by-step 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.