Can you help me with this word problem?

Question

it takes nine hours for Isabella to rake leaves by herself, but her brother Matthew can work three times as fast. If they work together, how long will it take them to rake leaves?

Answer 1

Hannah, this is a toughie, but I think we can do it!

 

If Matthew works three times as fast as Isabella, then he must be able to rake leaves in 3 hours by himself.

 

This means that in one hour, Isabella is going to get 1/9 of the job done and Matthew is going to get 1/3 of the job done.

 

If we let x = the time, then we combine their times.  1/9x + 1/3x = 1

 

What is the common denominator? 9, so 1/9x + 3/9x = 1

 

4/9x = 1

 

Dividing both sides by 4/9, we get x = 9/4 = 2 1/4 = 2 hours and 15 minutes.

 

Hope this helps!