A metal company's old machine makes bolts at a constant rate of 100

Total bolts in 1 hour of both machines: 250
So 300 bolts/250 bolts=6/5
60/5*6= 72 minutes

In one hour, they'll do 250 bolts. There are still 50 missing, and since they make 250 per hour, they'll need 50/250 * 60 (minutes) = 12 minutes to do the remaining 50 bolts.

Hence, B.

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:

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

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

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.

Efficiency of Old Machine = 100
Efficiency of New Machine = 150

Thus, Efficiency of Old + New Machine = 250

So, The machine will produce 300 bolts in 1.xx Hours

1 Hour = 60 min , so the Answer must be a few minutes more than 60 min, Among the given options only (B) matches, Answer must be (B) 72

We can let t = the number of hours to produce 300 bolts and create the equation:

(100 + 150) x t = 300

t = 300/250 = 6/5 hours, which is 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

In an hour, we will have 100 bolts from old machine and 150 from the new machine. So we have 250 from 300 in 60 minutes.

The only viable option is 72minutes.

120 minutes, the next option, will be like 500 bolts and we don't need that.

Hey guys

100 bolts per hour + 150 bolts per hour = 250 bolts per hour

Thats 250 bolts per 60 minutes

\(\frac{250}{60} = \frac{25}{6}\)

25 bolts are made every six minutes by the two machines working together

Make an equation to find how many minutes it takes to make 300 bolts

\(\frac{25}{6} = \frac{300}{x}\)

Multiply the diagonals

25x = 1800

Some quick long division

1800/25 = 72

The answer is (B)

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