Water can be pumped from a 100,000 gallon tank at a uniform rate by op

Question

Water can be pumped from a 100,000 gallon tank at a uniform rate by opening valve V, valve W, or both. The rate at which water is pumped out by opening valve V is 10,000 gallons per hour. If the tank is completely full and both valves are opened, the tank can be drained in 6 hours. How long would it take to empty the tank if it were 80% full and only valve W were opened?

A. 6 hours

B. 8 hours

C. 12 hours

D. 15 hours

E. 18 hours

Show Answer

Official Answer

C

A. 6 hours

B. 8 hours

C. 12 hours

D. 15 hours

E. 18 hours

rajatchopra1994 · Answer

Explanation:

Rate of V is 10000 gallons per hour
Valve V empty tank in = 100000/10000 = 10 hours.
Both valves empty tank in 6 hours

So Eqn will be :

1/w + 1/v = 1/b
1/w = 1/b - 1/v
1/w = 1/6 - 1/10
1/w = 4/60
w = 15 Hours.

So valve w alone will empty the tank in 15 hours.
So valve w alone empty 80% of tank = 0.8x15 = 12 Hours
IMO-C

Akp880 · Answer

Water can be pumped from a 100,000 gallon tank at a uniform rate by opening valve V, valve W, or both. The rate at which water is pumped out by opening valve V is 10,000 gallons per hour. If the tank is completely full and both valves are opened, the tank can be drained in 6 hours. How long would it take to empty the tank if it were 80% full and only valve W were opened?

A. 6 hours

B. 8 hours

C. 12 hours

D. 15 hours

E. 18 hours

Show Answer

Official Answer

C

A. 6 hours

B. 8 hours

C. 12 hours

D. 15 hours

E. 18 hours

Explanation:

Pump our rate for V=10000 gallon per hour
100000 gallon Tank water will be pumped out by V in=10000/10000 hrs= 10 hrs

Let the time taken by W to pump out water of whole tank be W hrs
then as per given information,

1/V+1/W=1/6

1/10+1/W=1/6

W=15 hrs

i.e  W takes 15 hrs to pump out 100000 gallon water

time taken by W to pump out 100000*0.8 gallon water= (15/100000)*100000*0.8
= 12 hrs

Hence C is the correct answer.

ramlala · Answer

6 Hrs to empty 100,000 gallon
Valve V pumped out 60,000 gallon in 6 Hrs.
Valve W pumped out 40,000 gallon in 6 Hrs.

We need ans for time required for valve W to pump out 80,000 (80%) gallon
Its 6x2=12 Hrs.

Ans: C

QuantMadeEasy · Answer

Step 1: Understanding the question 
Volume of tank = 100,000 gallon
Let rate of value V be v and rate of valve W be w
v = 10,000 gallons per hour

Step 2: Calculation 
When tank is full, Work = 100,000 gallon, Time to drain = 6 hours, Combined rate = (v+w) = (10000+w)
Using Rate * Time = Work equation
(10,000+w) * 6 = 100,000
w = (100,00/6) - 10,000 = 40,000/6 = 20,000/3

When tank is 80% full, Work = 80,000 gallon, Time to drain = t hours, Combined rate = w = 20,000/3
Using Rate * Time = Work equation
20,000/3 * t = 80,000
t = 12hours

C is correct

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daniformic · Answer

10000*6+x*6=100000 -> x=6667
80000/6667≅12

Answer C

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Water can be pumped from a 100,000 gallon tank at a uniform rate by op

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