BTGModeratorVI wrote: ↑

Wed Dec 16, 2020 12:43 pm

On a certain Monday, Carlos drove to work at an average speed of 50 miles per hour and home from work along exactly the same route at an average speed of 70 miles per hour. Which of the following is closest to his average speed for both trips combined?

A. 58.3 miles per hour
B. 60.0 miles per hour
C. 62.6 miles per hour
D. 65.4 miles per hour
E. It cannot be determined from the information given

Answer: A
Source: Veritas Prep

Average speed = (TOTAL distance)/TOTAL travel time)

Let d = the distance from work to home

Carlos drove to work at an average speed of 50 miles per hour
Time = distance/speed
So, travel time TO work = d/50 hours

Carlos drove home from work at an average speed of 70 miles per hour
So, travel time FROM work = d/70 hours

So, TOTAL travel time = d/50 + d/70
= 7d/350 + 5d/350 [rewrite with common denominators]
= 12d/350

Also, TOTAL distance = d + d = 2d

Which of the following is closest to his average speed for both trips combined?
Average speed = (TOTAL distance)/TOTAL travel time)
= (2d)/(12d/350)
= (2d)(350/12d)
= 700d/12d
= 700/12
= 350/6

STOP.
Since 360/60 = 60, we know that 350/6 will be LESS THAN 60

Answer: A

Cheers,
Brent