1. Bill can paint a closet in 2 hours. Bob can paint the same closet in 3 hours. How long will it take them to paint the closet working together? (I'm guessing 1 hour, or an hour & a half?)
Ok, this is about reciprocals.
If Bill can paint a closet in two hours, he can paint half a closet an hour right?
And if Bob can paint one in 3 hours, he can paint a third of a closet an hour.
Working together they can paint 1/2 + 1/3 = 5/6 of a closet an hour.
To find how many hours they take to paint the whole closet divide:
the number of closets to be painted/the number they can paint in an hour This is: 1/(5/6) = 6/5 of an hour = 1.2 hours =
1 hour and 12 minutesThe principle is exactly the same for the grass mowing one and pool draining one.
Hope that helps (and makes sense!)
Ahh I have time to spare and I'm bored, I'll do another:
4. One pipe can fill a tank in 4 hours. A second pipe also requires 4 hours, but a third needs three hours. How long will it take to fill the tank if all three pipes are open?
Slightly harder, but the principle is exactly the same.
Call the first pipe A the second B, and the third C..
Both A and B can fill the tank in 4 hours, so in one hour they can fill a quarter of it.
Pipe C can fill a third of the tank in an hour.
So if they all work together they can fill 1/4 + 1/4 + 1/3 = 5/6 of the tank in an hour.
And actually I now realise the answer is gouing to be exactly the same as it was for the first question as we have the same fraction.
1 hr 12 mins