Word problem

Question

Martha can rake the leaves in 5 hours. Her brother can do it in 3 hours. How long will it take them to do the job together?

Answer 1

Hi Rachel,

 

I've always kind of hated these questions, because the approach to solve them is not always intuitive. The key is turning each of the given values into a "rate" - not how long it takes them to rake, but how much can they rake in a certain amount of time.

 

     Martha rakes 1 yard per 5 hours: 1 yard

                                                     5 hrs

 

     Brother rakes 1 yard per 3 hours: 1 yard

                                                       3 hrs

 

Together, each hour, they can rake 1 yard/5 hours + 1 yard/3 hours.

 

     Finding common denominators, 1yard/5hrs + 1yard/3hrs = 3yards/15hrs + 5yards/15hrs = 8yards/15hrs

 

Together, they can rake 8 yards/15 hours. Now let's invert the fraction to find out how long it takes to rake 1 yard:

 

     15 hrs / 8 yards = 1.875 hrs / yard

 

So together, it would take them 1.875 hrs (or 1 hr, 52.5 mins) to rake 1 yard.

 

I hope this helps!

 

Andy