Sam can complete a certain task in 4 hours while Peter needs only 3 ho

Let the total work be 24 units

Efficiency of Sam is 6 units/hour
Efficiency of Peter is 8 units/hour

Work completed by Sam in half hour is 3 units, work left is 21 units

Combined efficiency of Sam and Peter is 14 units, so time required to complete the remaining piece of work is \(\frac{21}{14}\) = \(\frac{3}{2}\) Hours

Answer will be (A)

Less than a minute to solve: Break the problem into two stages. Use RT = W

Rates in jobs per hour:
Sam's rate (use in Stage 1): \(\frac{1}{4}\)
Peter's rate: \(\frac{1}{3}\)
Combined rate (use in Stage 2):
\((\frac{1}{4}+ \frac{1}{3})=\frac{7}{12}\)

Convert Sam's time working alone:
30 minutes = \(\frac{1}{2}\) hour*

Stage 1: Sam works alone

Total work is 1 (job)
How much work did Sam finish in 30 minutes?

R*T = W
R = \(\frac{1}{4}\)
T = \(\frac{1}{2}\) hour
\((\frac{1}{4}*\frac{1}{2})=\frac{1}{8}\)
of work is finished by Sam

How much work remains?
(Total W - Sam's W)
\((1-\frac{1}{8})=\frac{7}{8}\) of work remains for both to finish

Stage 2: they work together
How many hours will they need to finish the rest of the work?

R*T = W
R (combined, above): \(\frac{7}{12}\)
T = ?
W = \(\frac{7}{8}\)
\(\frac{7}{12}*T=\frac{7}{8}\)
\(T=(\frac{7}{8} * \frac{12}{7}) = \frac{12}{8}=\frac{3}{2}\)

Answer A


*\((30.mins*\frac{1hr}{60.mins})=\frac{30hr}{60}=\frac{1}{2}\) hour

We can let Sam’s rate = 1/4, and Peter’s rate = 1/3.

We can let the time Sam worked = 1/2 + x and the time Peter worked = x

Thus:

1/4(1/2 + x) + 1/3(x) = 1

1/8 + x/4 + x/3 = 1

Multiplying the entire equation by 24, we have:

3 + 6x + 8x = 24

14x = 21

x = 21/14 = 3/2 hours

Answer: A

I'm a bit thrown off by the wording of the question, particularly "to complete the task together?" Notably, it doesn't say "complete the remainder of the task together" nor does it say "complete the task working together" (which would also be ambiguous as you could read it as the time as though Sam did not already spend 30 min on it), so I'm reading this as the total time, including the 30 minutes Sam spends alone.

Bunuel, thoughts?

Rate of Sam =1/4
Rate of peter=1/3
in 30 minutes, sam would have completed 1/8 of the work-->1/2*1/4=1/8
remaining 7/8 work has to be completed together
combined rate=7/12-->7/12 * X=7/8
ans=3/2 --option (A)

I made the same "mistake." At least don't make another answer 2, which is what I selected because the entire job took two hours.

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