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Water flows into a 25-liter bucket through a hose and out through a ho 24 May 2018, 06:08
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74% (01:52) correct 26% (02:01) wrong based on 166 sessions

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Water flows into a 25-liter bucket through a hose and out through a hole in the bottom of the bucket. The rate of flow through the hose is 1 liter per minute. If the bucket is filled to capacity in 40 minutes, at what rate, in liters per minute, was water flowing out of the bucket through the hole?


A. \(\frac{3}{8}\)

B. \(\frac{3}{5}\)

C. \(\frac{5}{8}\)

D. \(\frac{8}{5}\)

E. \(\frac{13}{8}\)
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A
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Water flows into a 25-liter bucket through a hose and out through a ho 24 May 2018, 12:48
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Bunuel
Water flows into a 25-liter bucket through a hose and out through a hole in the bottom of the bucket. The rate of flow through the hose is 1 liter per minute. If the bucket is filled to capacity in 40 minutes, at what rate, in liters per minute, was water flowing out of the bucket through the hole?


A. \(\frac{3}{8}\)

B. \(\frac{3}{5}\)

C. \(\frac{5}{8}\)

D. \(\frac{8}{5}\)

E. \(\frac{13}{8}\)

The total capacity of the bucket is 25 liters.

If the hose fills 1 liter in a minute, in 40 minutes it would fill 40 liters. In 40 minutes the
bucket is filled to capacity, so the hole in the bottom would have emptied 15 liters in the
40 minutes.

Therefore, the rate of the water flowing out of the bucket through the hole in a minute is \(\frac{15}{40} = \frac{3}{8}\)(Option A)
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Water flows into a 25-liter bucket through a hose and out through a ho 24 May 2018, 13:39
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Bunuel
Water flows into a 25-liter bucket through a hose and out through a hole in the bottom of the bucket. The rate of flow through the hose is 1 liter per minute. If the bucket is filled to capacity in 40 minutes, at what rate, in liters per minute, was water flowing out of the bucket through the hole?


A. \(\frac{3}{8}\)

B. \(\frac{3}{5}\)

C. \(\frac{5}{8}\)

D. \(\frac{8}{5}\)

E. \(\frac{13}{8}\)


Total capacity = 25 litre
inflow rate = 1 litre /minute
outflow rate = x(say)

It takes 40 minute to completely fill the bucket of capacity 25 litre, hence the efficiency of filling the bucket = 25 / 40 = 5/8
so inflow rate - outflow rate = 5 / 8
==> 1 - x = 5 / 8
==>x = (8 - 5) / 8 = 3 / 8

A is the correct answer
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Water flows into a 25-liter bucket through a hose and out through a ho 28 May 2018, 19:39
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Bunuel
Water flows into a 25-liter bucket through a hose and out through a hole in the bottom of the bucket. The rate of flow through the hose is 1 liter per minute. If the bucket is filled to capacity in 40 minutes, at what rate, in liters per minute, was water flowing out of the bucket through the hole?


A. \(\frac{3}{8}\)

B. \(\frac{3}{5}\)

C. \(\frac{5}{8}\)

D. \(\frac{8}{5}\)

E. \(\frac{13}{8}\)

We can let the rate leaving the bucket = n, so the net rate is 1 - n. We can create the equation:

(1 - n) x 40 = 25

40 - 40n = 25

15 = 40n

15/40 = 3/8 = n

Alternate Solution:

At 1 liter per minute, the hose provides 40 liters of water. Since the bucket has a capacity of only 25 liters, 40 - 25 = 15 liters of water has flown out of the bucket through the hole. If 15 liters of water was let out in 40 minutes, we can find the rate of the water flowing out of the bucket using a simple proportion: Let x be the amount of water leaving the bucket in one minute (i.e. the rate).

x/1 = 15/40 = 3/8

Answer: A
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Water flows into a 25-liter bucket through a hose and out through a ho 01 Jun 2018, 03:21
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Bunuel
Water flows into a 25-liter bucket through a hose and out through a hole in the bottom of the bucket. The rate of flow through the hose is 1 liter per minute. If the bucket is filled to capacity in 40 minutes, at what rate, in liters per minute, was water flowing out of the bucket through the hole?


A. \(\frac{3}{8}\)

B. \(\frac{3}{5}\)

C. \(\frac{5}{8}\)

D. \(\frac{8}{5}\)

E. \(\frac{13}{8}\)


In these type of questions, ensure to differentiate between Positive work done & Negative work done & then establish relations between the given data.

Given Capacity of Bucket = 25 Litres

Rate of Hose to fill the bucket = 1 lit/min

Hence in 40 mins the hose can fill upto 40 litres.

Also, there is a hole at the bottom of the bucket, which is draining the water out, lets say at X litres/min.

Water drained by the hole in 40 mins is 40X litres.

Since the Capacity of bucket is 25 litres.

The resultant of the hose filling the bucket & the hole draining the bucket, both for 40 mins, fills the bucket to its capacity.

Consider filling the bucket as Positive work & draining the bucket as negative work.

we get, 25 = 40 - 40X

solving we get X = 3/8 litres per min

Answer choice A
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Water flows into a 25-liter bucket through a hose and out through a ho 18 Jul 2019, 08:38
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