Basically how much snow can be produced

Question

A ski resort can manufacture enough machine-made snow in 8 h to open its steepest run, whereas it would take 24 h of naturally falling snow to provide enough snow. If the resort makes snow while it is snowing naturally, how long will it take until the run can open?

Answer 1

This is basically the same idea as two people working

together to complete a job... We know how long it takes

either individually to complete the job and we wish to

know how long it takes with them working together.

 

The machine takes 8 hours so it does 1/8 of the snow per hour.

Nature takes 24 hours so it does 1/24 of the snow per hour.

 

Take the total per hour (1/8 + 1/24) multiplied by x hours

and set that equal to 100% of the job:

 

x(1/8 + 1/24) = 100%

x(1/8 + 1/24) = 1

x(3/24 + 1/24) = 1

x(4/24) = 1

x(1/6) = 1

x = 6 hours to open the run

 

Note that this makes sense because the machine will take less

time than 8 hours because it is being assisted by the natural snow fall.