A metal company's old machine makes bolts at a constant rate

[BTGmoderatorLU]

Source: GMAT Prep

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?

A. 36
B. 72
C. 120
D. 144
E. 180

The OA is B

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Hi All,

The answer choices to this question provide a fantastic shortcut. With the two machines that we're given, we know that...

Old Machine = 100 bolts/hour
New Machine = 150 bolts/hour

If they start at the same time, the two machines will create 250 bolts/hour

The question asks how long it would take the two machines to make 300 bolts, so we know it's going to be more than 1 hour.

If the two machines worked for 2 hours, then they'd make 500 bolts, but that's too many bolts.

We need an answer that's more than 1 hour, but less than 2 hours. The question also asks for an answer IN MINUTES. The ONLY answer that fits is the one that's between 60 minutes and 120 minutes.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[fskilnik@GMATH]

Source: GMAT Prep

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?

A. 36
B. 72
C. 120
D. 144
E. 180

\[?\,\,\, = \,\,\,T\,\,\left[ {\min } \right]\]

Perfect opportunity for UNITS CONTROL, one of the most powerful tools carefully explained in our course!

\[300\,\,{\text{bolts}}\,\,\,\,{\text{ = }}\,\,\,\,\left( {\frac{{100\,\,{\text{bolts}}}}{{60\,\,\min }}} \right)\,\, \cdot \,\,T\,\,\min \,\,\, + \,\,\,\left( {\frac{{150\,\,{\text{bolts}}}}{{60\,\,\min }}} \right)\,\, \cdot \,\,T\,\,\min \]
\[300\,\,\, = \,\,\,\frac{{5 \cdot \boxed2}}{{3 \cdot \boxed2}}T\,\, + \,\,\frac{{5 \cdot \boxed3}}{{2 \cdot \boxed3}}T\,\,\, = \,\,\,\frac{{25}}{6}T\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,T = \frac{6}{{25}}300 = 6 \cdot 3 \cdot 4 = 72\]

The correct answer is therefore (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

[Scott@TargetTestPrep]

Source: GMAT Prep

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?

A. 36
B. 72
C. 120
D. 144
E. 180

The OA is B

We can let t = the time, in hours, the machines work together; thus:

100t + 150t = 300

250t = 300

t = 30/25 = 6/5 hours, which is 6/5 x 60 = 72 minutes.

Alternate Solution:

We note that the two machines working together will produce 100 + 150 = 250 bolts in 60 minutes. Also, we notice that in 120 minutes, the two machines will produce 250 x 2 = 500 bolts. Since 300 is between 250 and 500, the time necessary for the two machines to produce 300 bolts must be between 60 and 120 minutes; the only possible choice is 72 minutes.

Answer: B