It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn? A. 16 B. 20 C. 36 D. 45 E. 90
(B) The easiest way to solve work-rate problems is to find a rate per unit of time. If it takes John 30 minutes to rake the lawn, then he can rake 1/30 of the lawn per minute. Todd can rake 1/60 of the lawn per minute. Together they can rake 1/60 + 1/30 = 1/60 + 2/60 = 3/60 = 1/20 of the lawn per minute.
If they rake 1/20 of the lawn per minute, it will take them 20 minutes to rake the lawn together.
The correct answer is choice (B). --------- Averages makes no use in this question, better to calculate the lawn per unit.
Averages makes no use in this question, better to calculate the lawn per unit.
We do NOT deal with average values in this problem. First, we calculate the rates (the lawn per unit). Then we calculate the combined rate (the sum, NOT average). In the end, we calculate the required time.
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