Three machines, K, M, and P, working simultaneously and

Question

Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes.
(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes.

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Official Answer

A

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Depaulian · Answer

From the data provided in the Q

1/k + 1/m + 1/p = 1/24

(1) says 
1/m + 1/ p = 1/36
which along with the eq from the Qs, gives
1/k = 1/24 - 1/36 = 1/72

means k will take 72 mins ,working alone at its constant rate, to complete the task

(2) says
1/k + 1/p = 1/48
from this data , we can ind the working rate of m/c M.

So (1) alone is sufficient

viks4gmat · Answer

buddy... in the exam you wouldnt want to actually sit and <solve> such problems. In some DS questions u can conclude without actually solving them... this is one such type of a problem

if u really want a detailed explanation, here it is...

let mc K do the task individually in k mins
similarly P in p mins
and M in m mins

so K's work in 1 min is 1/k
M's work similarly is 1/m
and P's is 1/p

since working together they can complete the work in 24 mins, they complete 1/24th work in 1 min

= > 1/k + 1/m + 1/p = 1/24 ------ (1)

the remainder of the part, is pretty much the same as Depaulian has suggested. hence ans is A

smthsteve6 · Answer

all three working together it is 24

so 1/K+1/M+1/P = 1/24

1. 1/M+1/P = 1/36

Applying this we can find 1/k

2. WE cannot fin 1/K with this

Ans A

Lstadt · Answer

Can someone please explain the reasoning behind flipping them like that?

I know that the amount of work produced is Rate * time = work. How is that used in this answer?

Thank you

ashiima · Answer

This is a gr8 explanation- thanks i missed the qs

BDSunDevil · Answer

1/k+1/M+1/p=1/24. K=?

Statement 1: we have value for 1/M+1/P. Can solve for K. Sufficient.
Statement 2: we have value for 1/K+1/P. Can solve for M but not for K. Not sufficient.

Bunuel · Answer

Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

Say k, m, and p are the numbers of minutes machines K, M, and P take, respectively, to complete the task. Then we have that \(\frac{1}{k}+\frac{1}{m}+\frac{1}{p}=\frac{1}{24}\).

(1) Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes --> \(\frac{1}{m}+\frac{1}{p}=\frac{1}{36}\), thus \(\frac{1}{k}+\frac{1}{36}=\frac{1}{24}\) --> we can find the value of \(k\). Sufficient.

(2) Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes --> \(\frac{1}{k}+\frac{1}{p}=\frac{1}{48}\). The value of k cannot be determined from the data we have. Not sufficient.

Answer: A.

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