You can do one-half of a job in an hour. Your friend can do one-third of the same job in an hour. How long will it take to do the job if you work together? Write your answer as a decimal.

Question

You can do one-half of a job in an hour. Your friend can do one-third of the same job in an hour. How long will it take to do the job if you work together? Write your answer as a decimal.

Answer 1

working alone one does 1/2 the job in one hour, the other does 1/3 of a job in one hour

working alone one does a full job in two hours, the other does a full job in 3 hours

in one hour

1/2 + 1/3 = 1/x

5/6 = 1/x

cross multiply

5x = 6

x = 6/5 = 1.2 hour working together

if each did the full job in 2 hours, together they'd do it in half that time or 1 hour

if each did the full job in 3 hours, together they'd do it in half that time or 1.5 hours

together they'd do it somewhere between 1 and 1.5 hours

a simple average would be (1+1.5)/2 = 2.5/2 = 1.25, which is close to 1.2

but you want a weighted average, so the faster person's time gets greater weight

pulling the average down a little

(3(1) + 2(1.5))/(2+3) = (3+3)/5 = 6/5 = 1.2