Basic Work Problem

007Bond · New Member Offline Joined: 13 Aug 2009 Posts: 2

Peter mows the lawn in 40 minutes and John mows takes 60 minutes to mow the same lawn. How long will it take for them both to mow the same lawn?

**Posted:** Sat Oct 31, 2009 8:51 am

isabella2296

Peter can mow a lawn in 40 minutes = 2/3 of an hour. That means he mows 1.5 lawns in one hour. Similarly, John mows one lawn per hour. Together, then, they mow 2.5 lawns, so it takes them 60/2.5 = 24 minutes.

**Posted:** Sat Oct 31, 2009 8:59 am

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fishythefish

For problems like this, a general formula is

$\frac{n}{\frac{1}{r_1}+\frac{1}{r_2}}$

where $n$ is the number of objects (in this case, lawns needed to be mowed), and $r_1$ and $r_2$ are the rates the people work at. If there are $x$ people working, the denominator is $\frac{1}{r_1}+\frac{1}{r_2}+...+\frac{1}{r_x}$

Or if you know sigma notation, $\displaystyle\sum_{i=1}^{x}\frac{1}{r_i}$

**Posted:** Sat Oct 31, 2009 9:19 am

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