Roland and Sam wash dogs to make extra money. Roland can wash all of the dogs in 4 hours. Sam can wash all of the dogs in 3 hours. How long will it take them to wash the dogs if they work together?

Question

1/7 hours
1 5/7 hours
1/12 hours
7/12 hours

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Answer 1 · 2017-03-20T20:57:42

The second answer is the correct one (#1 5/7# hours).

This problem seems difficult until we try the approach if considering what fraction of a dog each can wash each hour. Then it becomes fairly simple!

If Roland washes all the dogs in four hours, he does one quarter of the dogs each hour.

Similarly, Sam does one third of the dogs each hour.

Now, we add #1/4 + 1/3# to get #7/12# of the dogs washed each hour, by the two boys working together.

So, inversely, it takes them #12/7# of an hour (#1 5/7# hour) to wash all the dogs.