Two hoses are pouring water into an empty pool. Hose 1 alone would fil

Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 4 hours. How long would it take for both hoses to fill up two-thirds of the pool?

A. 5/12 hours
B. 5/8 hours
C. 8/5 hours
D. 12/7 hours
E. 12/5 hours

Solution -

Both hose 1 and 2 do the job in 1 hour is 1/6+1/4 = 5/12 --> 12/5 hours to complete the job.

Time takes to fill up two-thirds of the pool = (12/5)*(2/3) = 8/5 hours. ANS C.

METHOD-1

Hose 1 would fill the pool alone in 6 hours
i.e. 1 Hour work of Hose 1 = 1/6

Hose 2 would fill the pool alone in 4 hours
i.e. 1 Hour work of Hose 2 = 1/4

i.e. 1 Hour work of Hose1 and Hose2 together = (1/6)+(1/4) = (5/12)

i.e. (5/12) work can be finished by Hose1 and Hose2 together in 1 hour
i.e. (2/3) work can be finished by Hose1 and Hose2 together in 1*(12/5)*(2/3) = 8/5 hour

Answer: Option C

METHOD-2

Assume the Capacity of Tank that is Divisible by 4 and 6
Let, Capacity of Tank = 12 Units

i.e. Amount of water intake from Hose 1 in 1 hour = 12/6 = 2 Units
i.e. Amount of water intake from Hose 2 in 1 hour = 12/4 = 3 Units

i.e. Amount of water intake from Hose 1&2 together in 1 hour = 2 + 3 = 5 Units

2/3 of tank capacity = (2/3)*12 = 8 Units

Time taken by Hose 1&2 together to fill 5 units = 1 hour
i.e. Time taken by Hose 1&2 together to fill 8 units = 8/5 hour

Answer: Option C

Time taken by H1 =6, W=1,R1=1/6
Time taken by H2=4,w=1,R2 =1/4
so together R1+R2 =1/6+1/4= 5/12
and w=2/3, t= w/(R1+R2)= 2/3 *12/5 =8/5

Hence answer is C
Thanks,

both toghter to fill full tank = 1/6 +1/4 = 10/24=5/12 ... hence time required to fill full tank = 12/5

to fill 2/3 tank = 2/3* 12/5 = 8/5
Answer C

6*4/6+4 = 24/10 = 8/5 hours.
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MANHATTAN GMAT OFFICIAL SOLUTION:

If Hose 1 can fill the pool in 6 hours, its rate is 1/6 “pool per hour,” or the fraction of the job it can do in one hour. Likewise, if Hose 2 can fill the pool in 4 hours, its rate is 1/4 pool per hour. Therefore, the combined rate is 5/12 pool per hour (1/4 + 1/6 = 5/12):

RT = W
(5/12)*t = 2/3
t = 8/5 hours

Answer: C.
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together they fill 10 pools in 24 hours or 1 pool in 12/5 hours. Thus, 2/3 would be filled in 12/5 * 2/3 = 8/5

Hi All,

This question is a variation of a 'Work Formula' question (it involves 2 'entities' working on the same task together), so we can use the Work Formula to solve it.

Work = (A)(B)/(A+B) where A and B are the individual times that it takes the 2 entities to complete the task on their own.

Here, we're told that Hose 1 can fill a pool in 6 hours and that Hose 2 can fill the pool in 4 hours. We're asked how long it takes the two hoses to fill 2/3 of the pool...

To fill the ENTIRE POOL, it takes...

(6)(4)/(6+4) = 24/10 = 2.4 hours

To fill 2/3 of the pool takes 2/3 of the time. Since 2.4 hours = 12/5 hours, it would take...

(2/3)(12/5) = 24/15 = 8/5 hours to fill 2/3 of the pool.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

rate of hose 1 = 1/6
rate of hose 2 = 1/4

combined rate = 1/6 + 1/4 = 5/12

to cover the 2/3 of the pool time taken = 2/3 / 5/12 = 8/5 hrs

We see that the rate of hose 1 is 1/6 and the rate of hose 2 is 1/4. We can let x = time needed to fill 2/3 of a pool when they work together and create the equation:

1/6(x) + 1/4(x) = 2/3

Multiplying the equation by 12, we have:

2x + 3x = 8

5x = 8

x = 8/5 hours

Answer: C
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Workdone by Hose1 in an hour=1/6
Workdone by Hose2 in an hour=1/4
Workdone by Hose1 and Hose2 together in an hour=1/6+1/4=10/24 (work/hr)

10/24 of the workdone=1 hr
2/3rd of the workdone in hours-24*2/10*3=8/5 hrs.

(C)

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