SAT question:
Darly can complete a paper route in 20 mins. Bob can complete in 30mins. how long will it take both of them to complete the route if they work together, one starting at each end?

Question

SAT question:
Darly can complete a paper route in 20 mins. Bob can complete in 30mins. how long will it take both of them to complete the route if they work together, one starting at each end?

anonymous · Answer

what do you think the rate of each person is?

whpalmer4 · Answer

@sourwing has exactly the right idea: find the rate of each worker/machine/pipe, etc.  combine as appropriate for the problem.

Darly does 1 route/20 minutes = 1/20 of a route per minute
Bob does 1 route/30 minutes = 1/30 of a route per minute

Together, they do 1/20 + 1/30 of a route per minute.  Dust off your fraction skills and find $$\frac{1}{\frac{1}{20}+\frac{1}{30}}=$$which will be the number of minutes they take to do it together.

whpalmer4 · Answer

Every electrical engineer has encountered that calculation many times when computing the equivalent resistance of a pair of resistors in parallel: a shortcut that most of us remember is that $$\frac{1}{\frac{1}{a}+\frac{1}b} = \frac{a*b}{a+b}$$