Mary takes 4 hours to do her math homework and Joe takes 6 hours to do his math homework. How much time would it take if they did their homework together?

Question

I can't remember the formula to solve this type of problem.

Answer 1

Hi Aki--

 

The key is to figure out how much work each can do in ONE hour--their unit rate.

 

So Mary can do 1/4 in an hour, and Joe can do 1/6 in an hour.

 

Together in one hour they can do 1/4 + 1/6, or 5/12.

 

Since we're talking about pieces of hours here, think of everything in minutes, or 60ths of an hour. They can do 25/60 in an hour, which means they can do 50/60 in 2 hours, and then they'll have 10/60 left. If they did 50/60 in 2 hours, they can do the last 10/60 in one-fifth of 2 hours, which equals 24 minutes.

 

So... 2 hours and 24 minutes.

 

Hope this helps.

 

Matt in NY

Answer 2

Mary does 1/4 of her homework in 1 hour

Joe does 1/6 of his homework in 1 hour

x=# of hours doing homework together

(1/4)x+(1/6)x=1 (homework finished)

common denominator is 12

12(1/4)x+12(1/6)x=12(1)

3x+2x=12

5x=12

x=12/5

x=2.4 hours or 2 hours 24 minutes together