It would take 120 minutes for a leaky cold-water faucet to fill an

Question

It would take 120 minutes for a leaky cold-water faucet to fill an empty bucket. It would take 200 minutes for a leaky hot-water faucet to fill the same bucket. How many minutes would it take both faucets, leaking at their respective constant rates, to fill the empty bucket if they began leaking into the bucket at the same time?

A. 60
B. 75
C. 90
D. 105
E. 160

A. 60
B. 75
C. 90
D. 105
E. 160

KarishmaB · Accepted Answer

The concept being tested here is simply of two objects working simultaneously. One at the rate of 1/120th work/min and other at the rate of 1/200th work/min. Rates are additive so Total Rate = \frac{1}{120} + \frac{1}{200} = \frac{1}{75} So both together are doing 1/75th of the work so they will take 75 mins to complete it. Answer (B) Check out this video for work rate basics: https://youtu.be/88NFTttkJmA and this post for a more advanced question on these basics: https://anaprep.com/arithmetic-work-rat ... s-and-all/

gmatophobia · Answer

Assume  t_1  is the time taken by the leaky cold-water faucet to fill an empty bucket

Assume  t_2  is the time taken by the leaky hot-water faucet to fill an empty bucket

Time taken by both the faucets, leaking at their respective constant rates, to fill the empty bucket =  \frac{t_1 * t_2}{t_1+t_2}

= \frac{200 * 120}{320}

Divide the numerator and denominator by 80

= \frac{25 * 12}{4}

= 25 * 3

= 75

Option B

JeffTargetTestPrep · Answer

cold-water:

rate = work/time = 1/120 bucket/minute

hot-water:

rate = work/time = 1/200 bucket/minute

cold & hot water combined:

rate = rate₁ + rate₂ = 1/120 + 1/200 = 8/600 = 1/75 bucket/minute

time = work/rate = 1/(1/75) = 75 minutes

Answer: B

Paras96 · Answer

It would take 120 minutes for a leaky cold-water faucet to fill an empty bucket. It would take 200 minutes for a leaky hot-water faucet to fill the same bucket. How many minutes would it take both faucets, leaking at their respective constant rates, to fill the empty bucket if they began leaking into the bucket at the same time?

A. 60
B. 75
C. 90
D. 105
E. 160

Take the Volume of the bucket to be LCM (120,200) = 600 units
Rate of leaky cold-water faucet = 600/120 = 5
Rate of leaky hot-water faucet = 600/200 = 3

Total Rate = 3+5=8
Total time taken = Volume/Total rate = 600/8=75 minutes

Hence B

Vishnu0007 · Answer

Knowing the answer was 75, I intentionally chose 60 minutes, as it explicitly said "the faucets leaked into the bucket", although it isn't clear whether initially the faucets leaked into the bucket. We expect such tricks by GMAT on other questions and I guess I fell for this one too face first. But either way, what was the point of introducing the leaky concept?

GMATinsight · Answer

Let's Learn an EASY METHOD:

Let, Tank capacity = 600 Units

Leaky Cold-water faucet wok in 1 min = 600/120 = 5 Units
Leaky Hot-water faucet wok in 1 min = 600/200 = 3 Units

Combined rate of two faucets = 5+3 = 8 Units
Total Time to do whole work = 600/8 = 75 mins

Answer: Option B

NEYR0N · Answer

= 1/200 + 1/120 = 32/2400 = 4*8 /3*8*100 = 4/300 for rate. but for time its switched => 300/4 = you know that 28/4 is about 7 so 75 answer. 90 is way too big bc 36/4 = 9 ..

It would take 120 minutes for a leaky cold-water faucet to fill an

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