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MartyMurray
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Machines X, Y, and Z can complete a job in t hours. Updated on: 07 Mar 2026, 06:12
Originally posted by MartyMurray on 17 Aug 2025, 19:23.
Last edited by MartyMurray on 07 Mar 2026, 06:12, edited 3 times in total.
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Machines X, Y, and Z can complete a job in t hours. If machine X working alone can complete the job in s hours, machine Y can complete the job in 2s hours, and machine Z can complete the job in 3s hours, what is t in terms of s?

(A) 6s/11

(B) 2s

(C) 6s

(D) 11/6s

(E) 11s


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MartyMurray
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Machines X, Y, and Z can complete a job in t hours. 17 Aug 2025, 19:29
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Machines X, Y, and Z can complete a job in t hours. If machine X working alone can complete the job in s hours, machine Y can complete the job in 2s hours, and machine Z can complete the job in 3s hours, what is t in terms of s?

Let X, Y, and Z be the rates of the three machines.

Machines X, Y, and Z can complete a job in t hours.

X + Y + Z = 1/t

machine X working alone can complete the job in s hours, machine Y can complete the job in 2s hours, and machine Z can complete the job in 3s hours

X + Y + Z = 1/s + 1/2s + 1/3s

1/t = 1/s + 1/2s + 1/3s

1/t = 11/6s

t = 6s/11

(A) 6s/11

(B) 2s

(C) 6s

(D) 11/6s

(E) 11s

Correct answer: A
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Machines X, Y, and Z can complete a job in t hours. 18 Aug 2025, 19:22
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Matrix time!

Machine: R -*- T == W
X: ? -*- s == 1
Y: ? -*- 2s == 1
Z: ? -*- 3s == 1
XYZ: ? -*- t == 1

We can determine that machine x has a rate of 1/s, machine y has a rate of 1/2s, and machine z has a rate of 1/3s. To determine what rate they work together at we add all three rates together (1/s) + (1/2s) + (1/3s) for a common denominator of 6s. so we know we have

6/6s + 3/6s + 2/6s = 11/6s. Quick select D and move on. INCORRECT

We are being asked for t in terms of s not for the combined rate so:

11/6s * t = 1

divide 1 by 11/6s, or multiply 1 by 6s/11 to get t = 6s/11, answer choice A
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Machines X, Y, and Z can complete a job in t hours. 13 Apr 2026, 04:40
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Deconstructing the Question

Each machine completes the same job in a different amount of time, so we convert times into rates.

Machine X takes \(s\), Y takes \(2s\), and Z takes \(3s\).

We add the rates and then take the reciprocal to find the total time \(t\).

Step-by-step

Rate of X is \(\frac{1}{s}\).

Rate of Y is \(\frac{1}{2s}\).

Rate of Z is \(\frac{1}{3s}\).

Total rate is

\(\frac{1}{s} + \frac{1}{2s} + \frac{1}{3s}\)

Using common denominator,

\(\frac{6}{6s} + \frac{3}{6s} + \frac{2}{6s} = \frac{11}{6s}\)

So the total rate is \(\frac{11}{6s}\).

Taking the reciprocal,

\(\frac{6s}{11}\)

Answer: A
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