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

Question

Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2

A. 3/2
B. 12/7
C. 2
D. 31/14
E. 5/2

wilhelmus999 · Answer

Peter works at 4/3 of Sam's speed, so together at 1 + 4/3 = 7/3 times Sam's speed. When Peter joins, Sam would have 7/2 hours left on his own. So together: 3/7 * 7/2 = 3/2 hours.

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DavidTutorexamPAL · Answer

As the calculation looks straightforward, we'll just do it.
This is a Precise approach.

Sam works at a rate of T/4 and Peter at a rate of T/3.
Together they work at a rate of T/4+T/3 = 7T/12.
In half an hour Sam completes T/8 units of work so we can write:
7T/12 * hours = T - T/8 = 7T/8.
Simplifying gives 12/8 = 3/2 hours, answer (A).

Abhishek009 · Answer

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)

generis · Answer

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

ScottTargetTestPrep · Answer

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

bcl · Answer

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?

Bunuel , thoughts?

arockia · Answer

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)

ghostman23 · Answer

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.

Chokhani · Answer

Sam's 1/2 hr work=(1/8)x:
remaing work=7x/8
sam+peter 1 hr task=7x/12
sam +peter x in 12/7 
so, 7x/8 in 12/8 or 3/2 (a)

lily123400 · Answer

Was able to solve this in under 1 minute 30. 
Sam works for half an hour, and since he takes 4 hours we know that .5/4 is 1/8. so we are looking for time of doing 7/8 of work for the combined rate.
combined rate = 1/4 + 1/3 = 7/12
w=r(t)
(7/8) / (7/12) = t
t = 3/2

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

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