When Anne and Rebecca work together they can deliver the mai

When Anne and Rebecca work together they can deliver the mail in Oppelo AK in 5.5 hours. When Anne works alone she can deliver the mail in 0.5 hours more time than it takes Rebecca when she works alone. How long does it take each of them to deliver the mail when working alone?

Steps should have square roots and/or quadratic formula.

Solution

Let time taken by Rebecca alone to deliver the mail be T hours.

Then as per the question, time taken by Anne alone to deliver the mail is T + 0.5 hours.

If Anne and Rebecca both delivers the mail together then time taken by them to deliver the mail be 5.5 hours.

Therefore, we can write it as:

1/5.5 = 1/T + 1/(T+0.5)

Taking LCM on right hand side, we get:

1/5.5 = (T + 0.5 + T)/T(T+0.5)

Cross multiply, we get:

T² + 0.5T = 5.5(2T + 0.5)

T² + 0.5T = 11T + 2.75

T² - 10.5T - 2.75 = 0

T² - 105/10 T - 275/100 = 0

4T² - 42T - 11 = 0

T = (42 + 39.85)/8 or T = (42 - 39.85)/8

T = 10.20 hours or T = 0.27 hours

So, obviously answer is T = 10.20 hours as alone time will not be less than the time they take together to deliver.

Therefore, Rebecca takes 10.20 hours to deliver the mail alone.

Anne take 10.20 + 0.5 = 10.70 hours to deliver the mail alone.