A Metal Company's Old Machine Makes Bolts at a Constant Rate of 100 GMAT Problem Solving

Question: A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 300 bolts?

1. 36
2. 72
3. 120
4. 144
5. 180

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.
• The company's new machine makes bolts at a constant rate of 150 bolts per hour.
• Both machines start at the same time and continue making bolts simultaneously.

Find out:

• The time taken in minutes by the two machines to make a total of 300 bolts.

Let the time in hours the machines work together be t; therefore, we get,
=> 100t + 150t = 300
=> 250t = 300
=> t = 30/25 = 6/5 hours,
We need to divide ‘t’ by 60 to get the time in minutes.
Therefore, the time taken by the two machines to make a total of 300 bolts = 6/5 x 60 = 72 minutes.

Approach Solution 2:

The problem statement informs that:

Given:

• A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.
• The company's new machine makes bolts at a constant rate of 150 bolts per hour.
• Both machines start at the same time and continue making bolts simultaneously.

Find out:

• The time taken in minutes by the two machines to make a total of 300 bolts.

Let T minutes be taken by two machines to make a total of 300 bolts.
300 bolts = (100 bolts/60 min) * T min + (150 bolts/60 min) * T min
=>300 = (5*2 / 3*2)T + (5*3 / 2*3)T = (25/6)T
=>T = (6/25)* 300 = 6 * 3 * 4 = 72mins

Therefore, the time taken by the two machines to make a total of 300 bolts is 72 minutes.

Approach Solution 3:

The problem statement discloses that:

Given:

• A metal company's old machine makes bolts at a constant rate of 100 bolts per hour.
• The company's new machine makes bolts at a constant rate of 150 bolts per hour.
• Both machines start at the same time and continue making bolts simultaneously.

Find out:

• The time taken in minutes by the two machines to make a total of 300 bolts.

It is noted that two machines together will make = 100 + 150 = 250 bolts in 60 minutes.
Therefore, in 120 minutes, the two machines will create = 250 x 2 = 500 bolts.
Since 300 bolts lie between 250 and 500, the time required for the two machines to make 300 bolts must stand between 60 and 120 minutes.
Therefore, the most possible answer choice is 72 minutes.

“A metal company's old machine makes bolts at a constant rate of 100”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide 2021”. GMAT Problem Solving questions help the candidates to evaluate information and solve numerical problems. GMAT Quant practice papers enable the candidates to become familiar with varieties of questions that will improve their mathematical knowledge.

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