Distance/Rate Problems

swerve wrote: ↑

Fri Mar 27, 2020 10:34 am

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

The OA is C

Source: Official Guide

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)

Answer: C

Cheers.
Brent

swerve wrote: ↑

Fri Mar 27, 2020 10:34 am

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

The OA is C

Source: Official Guide

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