SOLUTION: Because of an anticipated heavy rainstorm, the water level in a reservoir must be lowered by 1 foot. Opening Spillway A lowers the level by this amount in 4 hours, whereas opening

Question 277017: Because of an anticipated heavy rainstorm, the water level in a reservoir must be lowered by 1 foot. 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 foot if both spillways are opening?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = units

the number of units is equal to 1 (lowering the level in the reservoir by 1 foot)

Spillway A can do the job in 4 hours.

The rate at which spillway A can do the job is equal to 1/4 which means that spillway A can lower 1/4 of a foot per hour.

Spillway B does the job in 6 hours.

The rate at which spillway B can do the job is equal to 1/6 which means that spillway A can lower 1/6 of a foot per hour.

If you open both spillways, then their rates are additive.

This means that:

(1/4 + 1/6) * T = 1 where T is the number of hours it will take when both work together.

Remove parentheses to get:

(1/4)*T + (1/6)*T = 1

Multiply both sides of this equation by 24 to get:

6*T + 4*T = 24

Simplify to get:

10*T = 24

Divide both sides of this equation by 10 to get:

T = 2.4

It should take 2.4 hours for both working together.

Plug into original equation to see if this is accurate.

(1/4)*2.4 + (1/6)*2.4 = 1.

Simplify to get:

.6 + .4 = 1 which is true confirming the values are good.

In the following graph, y represents the rate, and x represents the time.

You can see that

when x = 4, y = 1/4 which is the rate of spillway A.
when x = 6, y = 1/6 which is the rate of spillway B.
when x = 2.4, y = 10/24 which is the combined rate of spillway A and B.

1/4 + 1/6 = 10/24.

The horizontal lines on the graph are 10/24, 1/4, and 1/6 respectively going from top to bottom.

They correspond to the x values of 2.4, 4, and 6 respectively going from left to right.

When spillway A and spillway B work together, they can lower the level by 1 foot in 2.4 hours.

Since Rate * Time = Work (expressed in units produced), then:

R * 2.4 = 1 which results in R = 1/2.5 which is the same as 10/24 which is the combined rate of spillway A and spillway B.

RELATED QUESTIONS
Because of an anticipated heavy rain storm a reservoir needs to be lowered by 1 foot. If... (answered by josgarithmetic)

The reservoir behind Buford Dam can be emptied in 15 days by opening both of its... (answered by josgarithmetic)

During a rainstorm, 15 litres of water fell per square metre. By how much did the water... (answered by ikleyn)

There are 2 overflow pipes at a dam. The larger overflow pipe can lower the level of the (answered by josmiceli,Nate)

A reservoir containing 1 million gallons of water has been tainted with arsenic.... (answered by richwmiller)

ECOLOGY The water level of a reservoir is at 27 feet. During a drought the... (answered by tutorcecilia)

A rectangular water reservoir contains 42000 liters of water.Find the depth of water in... (answered by macston)

The height (in feet) of the water level in a reservoir over a 1 year period is modeled by (answered by nerdybill)

a solid cube of sides 50 cm is kept in an empty reservoir of length 3 metres, breadth 2... (answered by Fombitz)