Answer:
12 minutes
Step-by-step explanation:
You want to know the time it takes to wash 2 bushels of spinach when you work together if you can wash one in 10 minutes and your cousin can wash one in 15 minutes.
After 10 minutes, you have washed 1 bushel of spinach, and your cousin has washed 10/15 = 2/3 of a bushel of spinach. We can write a proportion for the time required to wash 2 bushels:
time/bushels = (10 min)/(5/3 bu) = t/(2 bu)
t = 2(10 min/(5/3)) = 20 min(3/5) = 12 min
You can wash two bushels of spinach in 12 minutes working together with your cousin.
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Additional comment
The combined rate in bushels per minute is ...
(1 bu)/(10 min) +(1 bu)/(15 min) = (3+2 bu)/(30 min) = 1/6 bu/min
The time for each bushel is the inverse of this: 6 min/bu.
Combining rates in this way is the conventional way to work this problem.
The answer to this question is called the "harmonic mean" of the two numbers 10 and 15. The harmonic mean of N numbers is N divided by the sum of their reciprocals.
