Question

Professor J can grade an entire section of essays in 3 hours. His teaching assistant, M, can grade the same amount of essays in 5 hours. How long would it take them to grade the essays if they work together?

(15points) plz help!

Answer 1

The time it takes them to grade the essays if they work together is 1.857 hours

Explanation:

• Let t1 is time taken by Professor J = 3 hours
• Let t2 is time taken by the assistant = 5 hours
• Let tb is the time taken by both

The formula for “Work” Problems that involve two persons is

`(1)/(t1) + (1)/(t2) =(1)/(tb)`

<=>
`(1)/(3) + (1)/(5) =(1)/(tb)`

<=>
`(1)/(tb) = (8)/(15)`

<=> tb =
`(15)/(8) = 1.875 hours`

The time it takes them to grade the essays if they work together is 1.857 hours