Question: Lawn Mowers

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When doing combined rate

Nck - February 26, 2019

When doing combined rate questions, is using (a*b)/(a+b) an appropriate solution rather than combining the rates?

For example, Rama's rate is 1/6 and Trudy's rate is 1/12 to get an answer of 4 days. I can use the method of x/6+x/12 and substitute each 'x' with 6 and 12 for (6*12)/( 6+12) to get 72/18=4 houses.

That's a perfectly valid

greenlight-admin - February 27, 2019

That's a perfectly valid solution.
The reason I don't teach that approach is that the test makers can easily invalidate the formula by making a few changes to the question (for example, one worker gets a 1-hour head start, or a third worker starts helping after some elapsed time, etc.)

I did this way, Brent.

Ravsan - September 9, 2020

I did this way, Brent.

Rate of Ernie + Bert = 1/120 ( converted 2 hrs into mins )

Rate of Kermit = 1/180 ( converted 3 hrs into mins )

If all three work together, rate is 1/120 + 1/180

Multiply by 3 and 2 respectively, to get 3/360 + 2/360 = 5/360 = 1/72.

Time = Output/Combined rate = 1/ 1/72 = 1*72/1= 72 Minutes.

Perfectly reasoned! Nice work

greenlight-admin - September 9, 2020

Perfectly reasoned! Nice work, Ravin!

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