Question

Three machines, A, B and C can be used to produce a product. Machine A takes 60 hours to produce a million units. Machine B is twice as fast as A. Machine C takes the same time as A and B together. How much time will be required to produce a million units using all three machines?

• A. 12 hours
• B. 10 hours
• C. 8 hours
• D. 6 hours

Hint:

Always convert time into work rates and then sum the rates to find combined time using \texttt{Time = Work / Total Rate}.

Answer 1

The Correct Option is C

Let the work = 1 million units = 1 unit of work Machine A: 60 hours → 1 unit $\Rightarrow$ Rate of A = $\frac{1}{60}$ Machine B: Twice as fast $\Rightarrow$ time = 30 hours Rate of B = $\frac{1}{30}$ Machine C: Takes same time as A and B together A and B together rate = $\frac{1}{60} + \frac{1}{30} = \frac{3}{60} = \frac{1}{20}$ So C’s time = 20 hours Rate of C = $\frac{1}{20}$ All 3 together: \[ \text{Total rate} = \frac{1}{60} + \frac{1}{30} + \frac{1}{20} = \frac{1 + 2 + 3}{60} = \frac{6}{60} = \frac{1}{10} \Rightarrow \text{Time} = \frac{1}{\frac{1}{10}} = \boxed{10 \text{ hours}} \] Oops! Wait — option (b) is 10 hours So: \[ \boxed{10 \text{ hours}} \]