suppose that one worker can shovel snow from a storefront si

suppose that one worker can shovel snow from a storefront sidewalk in 50 minutes and another worker can shovel it in 30 minutes. How long will it take if they worked together?

Solution

#1 does 1/50 of the job per minute.
#2 does 1/30
Together, 1/50 + 1/30 = 8/150 per minute
--> 150/8 minutes to do the job
= 75/4 minutes
--------------
Use the shortcut, product/sum
50*30/(50+30) = 1500/80
= 75/4 minutes