Word problem

Question

If Rachel were to paint her living room alone, it would take 4 hours.  Her sister Terri could the job in 6 hours.  How long would it take them working together?

Answer 1

Okay let's give this a try.....

 

Rachael can do the job in four hours, Terri in six.  That means that Terri does two thirds of the work that Rachel does in four hours  4/6  = 2/3.  

 

So if we add those rates together we have 1 2/3 people on a job. so we divide the four hours by the 1 2/3 people working on the job and we get 2.40 hours  that is two hours and .40 or 40% of 60 minutes, which calculates to 24 minutes.

 

So, 2 hours, 24 minutes

Answer 2

Rachel in one hour does 1/4 of the room.

Terri in one hour does 1/6 of the room.

 

Rachel in h hours does h/4 of the room.

Terri in h hours does h/6 of the room.

 

h/4 + h/6 = 1   (1 completed room)

 

Multiply both sides by the LCM and solve for h.