Carcass wrote:
A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened ?
(A) 3 hours
(B) 3 hours 30 minutes
(C) 4 hours 30 minutes
(D) 5 hours
(E) The reservoir will never be filled to the brim
To make things easier on ourselves, let's assign a "nice" value to the total volume of the reservoir.
Let's say the reservoir holds a TOTAL of
20 gallons
A rectangular reservoir is filled with water till one-fifth of the height of the reservoir.1/5 of
20 =
4So, the reservoir currently holds
4 gallons of water
If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. In other words,
4 gallons of water will drain out of the reservoir in one hour.
Rate = amount/time = (4 gallons)/(1 hour) = 4 gallons per hour
So the RATE at which water drains
out of the outlet =
4 gallons per hourIf the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hoursIn other words, it will take 2 hours for the inlet tap to add the additional 16 gallons of water it will take to fill the reservoir.
Rate = amount/time = (16 gallons)/(2 hours) = 8 gallons per hour
So the RATE at which water flows
into the reservoir =
8 gallons per hourIn how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened ?If the inlet tap is opened for 30 minutes (aka 0.5 HOURS), the amount of water flowing
into the reservoir = (0.5 hours)(
8 gallons per hour) = 4 gallons.
So, after 30 minutes, the volume in the reservoir =
4 + 4 = 8 gallons.
So in order to FILL the reservoir to the top, we must add an additional 12 gallons of water
Once the outlet is unplugged, we have water flowing IN at a rate of
8 gallons per hour, and we have water flowing OUT at a rate of
4 gallons per hourSo the NET EFFECT =
8 gallons per hour -
4 gallons per hour =
4 gallons per hourWe need to add an additional 12 gallons of water, and we are doing so at a rate of
4 gallons per hourTime = amount/rate
= (12 gallons)/(
4 gallons per hour)
= 3 hours
IMPORTANT: Now we must add the 30 minutes that elapsed before the outlet was unplugged.
We get 3 hours + 30 minutes
Answer: B
_________________
Brent Hanneson - founder of Greenlight Test Prep