Question

Nancy can mow a yard in 3 hours and Peter can mow it in 4 hours. Suppose they both work together, how long would it take to finish?

Answer 1

Let the total work be W.
Nancy can complete W in 3 hours => she can complete W/3 in 1 hour
Peter can complete W in 4 hours => he can complete W/4 in 1 hour

If both work together, total amount of work done in 1 hour = W/3 + W/4 = 7W/12

Let time taken to complete W when both working together be 't' hours
=> 7W/12 * t = W
=> t = 12/7
So time taken is 12/7 hours

Answer 2

Another way to look at is simply that the combined rate is the same as the sum of the individual rates:\[\frac{1}{3}+\frac{1}{4}=\frac{1}{x}\]Solve for x to get\[x=\frac{7}{12}\]Now just compute the hours using the 1/x:\[\frac{1}{\frac{7}{12}}=\frac{12}{7}hours\]