1. ## Story problem help...

I need some help with a simple story problem. I seem to have forgotten as when I'm in algebra I forget some basic math. So, could you please solve this and explain it to me step by step? Thank you so much!

"Alice can paint the house in 5 hours, and Bob can paint it in 7 hours. How long will it take them if they work together?"

2. Originally Posted by FatalSylence
I need some help with a simple story problem. I seem to have forgotten as when I'm in algebra I forget some basic math. So, could you please solve this and explain it to me step by step? Thank you so much!

"Alice can paint the house in 5 hours, and Bob can paint it in 7 hours. How long will it take them if they work together?"
This means Alice can paint 1/5 of the house in one hour, and Bob can paint 1/7 of the house in one hour, right? This brings us to the following equation:

Let x be the work done in a hour by both of them:

1/5 + 1/7 = x
7/35 + 5/35 = 12/35

That means in a hour, they can do 12/35 of the house.

Which means, the entire work can be done in 35/12 hours (since the amount done in a hour multiplied by the number of hours should give 1 or if you prefer $\displaystyle \frac {n}{n}$).

35/12 = 2.916 hours or 2 hours and 55 minutes rounded.

Voilà.

3. Thank you so much, Sodapop! I appreciate it greatly. =)