A certain factory produces machine parts at a constant rate of m part

Question

A certain factory produces machine parts at a constant rate of m parts per minute. As soon as k parts are produced, they are transported as a batch to a customer's facility. If it takes t minutes to transport a batch to the customer's facility, which of the following represents the number of minutes that elapse between the time when the factory begins to produce parts and the time when the first batch arrives at the customer's facility?

A. k + t/m

B. k+ m/t

C. k + mt

D. m/k + t

E. k/m + t

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Official Answer

E

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Bunuel · Answer

Producing k parts at a rate of m parts per minute would take k/m minutes. For example, producing 100 parts at a rate of 10 parts per minute would take 100/10 = 10 minutes.

An additional t minutes are needed to transport the batch to the customer's facility. Therefore, the total time that elapses between the factory beginning production and the first batch's arrival at the customer's facility is k/m + t minutes.

Answer: E.

gmatophobia · Answer

One way is to solve the question using the algebraic approach. Another approach is to assume values.

﻿A certain factory produces machine parts at a constant rate of  2  parts per minute. As soon as  10  parts are produced, they are transported as a batch to a customer's facility. If it takes  8  minutes to transport a batch to the customer's facility, which of the following represents the number of minutes that elapse between the time when the factory begins to produce parts and the time when the first batch arrives at the customer's facility?

Time to produce  10  parts =  \frac{10}{2} = 5  minutes 
 Time to transport  10  parts =  8  minutes  
 Total time elapsed =  8 + 5 = 13  minutes

A. k + t/m ⇒  10 +\frac{ 8}{2} = 10 + 4 = 14  ;  Eliminate

B. k+ m/t ⇒  10 + \frac{2}{8} 
eq 13  ;  Eliminate

C. k + mt ⇒  10 + (2*8) 
eq 13  ;  Eliminate

D. m/k + t ⇒  \frac{2}{10} + 8 
eq 13  ;  Eliminate

E. k/m + t ⇒  \frac{10}{2} + 8 = 13  ;  Answer

Option E

Kinshook · Answer

Given: A certain factory produces machine parts at a constant rate of m parts per minute. As soon as k parts are produced, they are transported as a batch to a customer's facility.

Asked: If it takes t minutes to transport a batch to the customer's facility, which of the following represents the number of minutes that elapse between the time when the factory begins to produce parts and the time when the first batch arrives at the customer's facility?

Time to complete production of first k parts = k/m minutes
Time to transport first batch to customer's facility = t minutes

The time when the factory begins to produce parts and the time when the first batch arrives at the customer's facility = k/m + t minutes

IMO E

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A certain factory produces machine parts at a constant rate of m part

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