Distance Problem

bobdylan wrote: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. What fraction of total time does A drive?

A drives for (100 miles)/(Speed of A) = 100/40 hours
B drives for (100 miles)/(Speed of B) = 100/50 hours
C drives for (100 miles)/(Speed of C) = 100/60 hours

Hence, total time = (10/4 + 10/5 + 10/6) = 10(1/4 + 1/5 + 1/6) = 10(15/60 + 12/60 + 10/60) = (15 + 12 + 10)/6 = 37/6 hours

Hence, required fraction = (10/4)/(37/6) = (10*6)/(4*37) = (5*3)/37 = 15/37

The correct answer is C.

bobdylan wrote: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. What fraction of total time does A drive?
a) 15/74
b) 4/15
c) 15/37
d) 3/5
e) 5/4

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: C

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