Word problems

Question

because of an anticipated heavy rain storm, the water level in a reservoir must be lowered by 1 ft. Opening spillway A lowers the level by this amount in 4 hours, whereas opening the smaller spillway B does the job in 6 hours. How long will it take to lower the water level by 1 ft if both spillways are opened?

Answer 1

Spillway A lowers the level by 1 foot every four hours, or 1/4 of a foot per hour. Spillway B lowers the level 1 foot every 6 hours, or 1/6 of a foot per hour. Opening both spillways, then, means adding together the speeds of the two spillways:

 

1 + 1 = 3 + 2 = 5

4    6    12  12   12

 

So the combined speed is 5/12 of a foot per hour, or 5 feet every 12 hours. If we want to know how long, at this speed, it would take to lower the level by one foot, then we do:

 

1 foot x 12 hours = 12 hours

    1        5 foot            5

 

Or, 12/5 of an hour, or 2 hours and 2/5, or 2 hours and 24 minutes