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# Help with Word Math problem 4?

John can dig a hole in 4 hours. Frank can dig the same size hole in 5 hours. Ed can dig the same size

hole in 6 hours, and finally Mary can do the same in 7 hours. The four people decide to work together

and dig a single hole. How long does it take? Show your evidence.

### 1 Answer

- iamxLv 61 decade agoFavorite Answer
John can dig a hole in 4 hours, so he can dig 1/4 in one hour

Frank can dig the same size hole in 5 hours. so he can dig 1/5 in one hour

Ed can dig the same size hole in 6 hours so he can dig 1/6 in one hour

Mary can do the same in 7 hours so she can dig 1/7 in one hour

when they work together, they can dig the hole in x hours, so they dig 1/x in one hour

1/4 + 1/5 + 1/6 + 1/7=1/x

equalize the denominators at 420

105/420 + 84/420 + 70/420 + 60/420 = 1/x

319/420 = 1/x

x=420/319

x=1,3 hours approx.