Math CentralQuandaries & Queries


Question from bob, a student:

T=(AB)/(A+B) using this formula t= time a,b representing each individual person
i mow my lawn and it takes me 30 minutes my friend joe it takes 3 times as long,how long would it takes us together using this formula

Hi Bob,

This is a question for which I would never use a formula. Formulas are much too easy to forget. For this and many similar problems I just remember to look at rates.

You mow the lawn in 30 minutes so your rate is 1 thirtieth of a lawn per minute (1/30 lawns/min). It takes Joe 3 times as long so it takes him 90 minutes and thus his rate is one ninetieth of a lawn per minute (1/90 lawns/min). Hence if you work together you can work at

1/30 + 1/90 lawns/min,

and 1/30 + 1/90lawns/minute.

But you want the number of minutes per lawn which is the reciprocal of lawns per minute so it will take you

(90x30)/(90 + 30)minutes/lawn.

Exactly what the formula says!


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