Problem Solving

mrigank_bhushan wrote:Someone Please help to solve this

A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round-trip?

(A) 32.0 (B) 33.0 (C) 34.3 (D) 35.5 (E) 36.5

We can solve this one quickly if we assign a "nice" distance between Mayville and Rome ("nice" means a distance that works well with 30 miles per hour AND 40 miles per hour)

So, let's say the distance between Mayville and Rome = 120 miles

Time = distance/speed
So, time from Mayville and Rome (at 30 mph) = 120/30 = 4 hours
Time from Rome to Mayville (at 40 mph) = 120/40 = 3 hours

Average speed = (total distance traveled)/(total time)
= (120 + 120)/(4 + 3)
= 240/7
= 34.something (if we use long division here, we'll stop once we get to the ones digit)
= C

Cheers.
Brent

Hi mrigank_bhushan,

Brent's solution is spot-on; it's exactly how I would solve the problem, so I won't rehash it here.

It's worth noting that this type of "weighted average" question is a classic in the realm of standardized testing, so you will likely see something just like it on your Official GMAT. If you're given just the two speeds to work with, then pick a distance that works well with both speeds and do the necessary calculations. With a basic drawing and a bit of math, you'll have the correct answer.

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

mrigank_bhushan wrote:Someone Please help to solve this

A car travels from Mayville to Rome at an average speed of 30 miles per hour and returns immediately along the same route at an average speed of 40 miles per hour. Of the following, which is closest to the average speed, in miles per hour, for the round-trip?

(A) 32.0 (B) 33.0 (C) 34.3 (D) 35.5 (E) 36.5

We can use the average rate formula: average = total distance/total time, and let the distance each way = 120 miles. (Note that we could use any number for the distance, but we have chosen the convenient number 120 because it is evenly divisible by both 30 and 40, making the arithmetic easier.)
average = 240/(120/30 + 120/40)

average = 240/(4 + 3) = 240/7 = 34.3

Answer: C