A, B, and C each drove 100-mile legs of a 300-mile course at speeds of

Time for A = 100/40 = 10/4

Time for B = 100/50 = 10/5

Time for C = 100/60 = 10/6

10/4 + 10/5 + 10/6 = 150/60 + 120/60 + 100/60

= 370/60

Time for A of total = 150/60 / 370/60 = 150/370 = 15/37

Answer choice C

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Let the each runner runs 600 miles...

So, Time taken by A is 15 ; Time taken by B is 12 & Time taken by C is 10

Thus, Total time taken is 15 + 12 + 10 = 37

Fraction of the total time did A drove is 15/37 , Answer must be (C)

A time 100/40 = 2.5 i.e 15/2

Total Time A+B+C= 2.5+6+5 = 18/5

15/2 / 18/5 = 15/37

Using time = distance/rate, we can create the following expression, where the numerator is the total time that A drove and the denominator is the total time driven by A, B, and C combined:

(100/40)/(100/40 + 100/50 + 100/60)

(5/2)/(5/2 + 2 + 5/3)

Multiplying by 6/6, we have:

15/(15 + 12 + 10) = 15/37

Answer: C

Hi All,

We're told that A, B and C each drive 100-mile legs of a 300-mile course at speeds of 40, 50 and 60 miles per hour, respectively. We're asked what FRACTION of the total drive time did A drive. This question can be solved in a couple of different ways; there's actually a great 'ratio shortcut' that can help you to avoid most of the math.

Since Person A drove his 1/3 of the distance SLOWEST, we know that he drove MORE than 1/3 of the DRIVE TIME. The three speeds (40 mph, 50 mph and 60 mph) are close enough to one another that we know Person A did NOT drive "most" of the time though. Knowing those deductions, let's consider the 5 answers...

Answer A: 15/74 - this is closer to 1/5; TOO SMALL
Answer B: 4/15 - this is a little more than 1/4; TOO SMALL
Answer C: 15/37 - this is a little more than 1/3; MATCHES what we're looking for
Answer D: 3/5 - this is 60% of the total; TOO BIG
Answer E: 5/4 - this is above 100%; TOO BIG (and not mathematically possible)

Final Answer:

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

Time take by A, t1 = 100/40
Total time, T = 100/40 + 100/50 +100/60

Required ratio/fraction = t1/T = 15/37

Total Time = \(\frac{100}{40} + \frac{100}{50} + \frac{100}{60}= \frac{37}{6}\)

Now, Time taken by A is \(\frac{5}{2}*\frac{6}{37}=\frac{15}{37}\), Answer must be (C)

Hi, could you help me understand the logic when you say The three speeds (40 mph, 50 mph and 60 mph) are close enough to one another that we know Person A did NOT drive "most" of the time though.

I couldn't comprehend the last bit

Hi Hoozan,

When thinking about that comparison, it might help to think of a simpler comparison first:

If the three speeds had all been the SAME, then each of the three drivers would have driven the SAME amount of time (because they each drove the same 100 miles of distance) - and Person A would have driven exactly 1/3 of that total time.

As we increase any of the individual speeds, the total amount of time driven by that Person would decrease. This means that Person B drove LESS of the total time than Person A did and Person C drove LESS of the total time than either Person A or Person B. By extension, Person A must have driven MORE than 1/3 of the total drive time (since the other 2 drivers drove LESS of that time). The issue is 'how much more?'

Looking at how the answer choices are written, we clearly have 3 answers that are smaller fractions and two answers that are much larger. Both Answers A and B are too small (they're less than 1/3 - and we know that we're looking for an answer that's MORE than 1/3). Answer C is more than a 1/3 but less than 1/2 (which is an answer that makes sense, given the comparison described above). Answer D is 60 PERCENT of the total drive time, which is a LOT - and that would mean that Person B and Person C would both have to have been driving a LOT faster than Person A was. However, the differences from 40mph to 50mph and from 40mph to 60mph aren't large enough to possibly lead to such a big disparity.

If you wanted to calculate the exact differences, then the math wouldn't be too difficult (you could use D = R x T) to find the exact values - but again, based on how the answers are written, you don't actually need to do that math to select the correct answer.

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

Contact Rich at: Rich.C@empowergmat.com

Thanks a lot Rich! This was extremely helpful

Posted from my mobile device

Time taken by A = 100/40 = 2.5
Time taken by B = 100/50 = 2
Time taken by C = 100/60 = 5/3

Total time = 2.5+2+5/3 = 37/6
A's share = \(\frac{5/2}{37/6}\)\( = 15/37\)

Option C.

This is a great example of how quant questions can be tackled in a number of different ways, and the best approach for each student depends on your strengths, weaknesses, pacing, and degree to which you're able to be nimble with numbers.

Three ways. First is quantitative REASONING. Third is QUANTITATIVE reasoning. Second is somewhere in between.

First, ballparking. This is how I would do it on a real test. Faster, easier, almost no chance of making a silly calculation error, and eliminating four answer choices makes this NOT a guess.
A is the slowest, so must account for more than 1/3 of the time.
Look at the answer choices. A and B are greater than 1/3, so they are out.
A can't account for more than the full time. E is out.
We are down to C and D. All three speeds were within 20% of the median. A can't have driven for 60% of the time, right? D is out.
Answer choice C.

Second, math using something other than 300 miles for the trip. Yeah, they told us that the total distance is 300 miles, but the question just asks us for a ratio and the ratios will apply regardless of the distances, so we can use whatever we want for the total distance to make our lives easier. I refer to this as a "Hidden Plug In" since there's no explicit variable but there's something we can make up that gives us a clear path to the solution. How about each person drives 600 miles instead of 100 miles?
A drives for 15 hours.
B drives for 12 hours.
C drives for 10 hours.
A drives for 15 of the 37 hours. 15/37.
Answer choice C.

Third, math (plus a tiny bit of ballparking) using the numbers they gave us.
A drives 100 miles at 40mph, so 2.5 hours.
B drives 100 miles at 50mph, so 2 hours.
C drives 100 miles at 60 mph, so 1.66667 hours. Let's just call this 1.7 and see if we get close enough.
Total time is 6.2 hours. A drove for 2.5.
\(\frac{2.5}{6.2}\) That's less than 1/2 but more than 1/3.
Answer choice C.


ThatDudeKnowsBallparking
ThatDudeKnowsHiddenPlugIn

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