Larry can build a model car in 3 hours, Moe can build the same car in

RULE: If a person can complete an entire job in k hours, then in ONE HOUR, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in ONE HOUR, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Larry can build a model car in 3 hours, Moe can build the same car in 4 hours, and Fred can build the car in 5 hours.
So, from the above rule, we can conclude that:
Larry can complete 1/3 of the job in ONE HOUR
Moe can complete 1/4 of the job in ONE HOUR
Fred can complete 1/5 of the job in ONE HOUR

If the two fastest boys work together, how much of the car can they build in one hour?
Since Larry and Moe can each complete more of the job (than Fred can) in ONE HOUR, we know that Larry and Moe are the two fastest boys
In ONE HOUR Larry completes 1/3 of the job
In ONE HOUR Moe completes 1/4 of the job
So, working together, they can complete (1/3 + 1/4 ) of the job
1/3 + 1/4 = 4/12 + 3/12 = 7/12

Answer: C

If Larry can do the model car in 3 hours, he will be able to finish 1/3rd of the car in an hour.
Similarly, Moe and Fred can finish 1/4rth and 1/5th of the car.

Larry and Fred are the 2 fastest boys.
They can finish a total of 7/12(1/3 + 1/4) of the work in an hour(Option C)

Lets say the car has 60 parts (lcm of 3, 4 and 5) in all ….
L can do 60 parts in 3 hrs means 20 parts / hr
Similarly, M can do 15 parts / hr
And F can do 12 parts / hr…

So the L + M (the fastest boys working together) can do 20 + 15 = 35 parts in an hour ..
So 35/60 = 7/12 in an hr …

Hit a Kudo if you like the approach
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Let the total work be 60

Efficiency of Larry is 20
Efficiency of Moe is 15
Efficiency of Fred is 12

The 2 fastest boys in terms of efficiencies are - Larry & Moe, and their combined efficiencies are 35.

So, part of the car build in 1 hour is \(\frac{35}{60}\) => \(\frac{7}{12}\)

Thus, in 1 hour , (C) \(\frac{7}{12}\) part of the car is built...
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Larry and Moe are the fastest boys.

Therefore,

1/3 + 1/4
4/12 + 3/12
7/12

Which is answer C

Larry and Moe are the two fastest boys. Larry’s rate is 1 car in 3 hours, or 1/3 car per hour. Moe’s rate is 1 car in 4 hours, or 1/4 car per hour. Thus, in one hour, Larry and Moe can build 1/3 + 1/4 = 4/12 + 3/12 = 7/12 of a car.

Answer: C
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Larry can build a model car in 3 hours, Moe can build the same car in 4 hours, and Fred can build the car in 5 hours.
So, from the above rule, we can conclude that:
Larry Rate 1/3
Moe Rate 1/4
Fred Rate 1/5

If the two fastest boys work together, how much of the car can they build in one hour?
Since Larry and Moe can each complete more of the job (than Fred can) in ONE HOUR, we know that Larry and Moe are the two fastest boys
In ONE HOUR Larry completes 1/3 of the job
In ONE HOUR Moe completes 1/4 of the job
So, working together, they can complete (1/3 + 1/4 ) of the job
1/3 + 1/4 = 4/12 + 3/12 = 7/12 ( Combined Rate )

Target Question how much of the car can they build in one hour?

Output in I hour = Time*Rate = 1* 7/12 = 7/12 (C )

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