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On a certain Monday, Carlos drove to work at an average

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On a certain Monday, Carlos drove to work at an average

by BTGmoderatorLU » Tue Jan 08, 2019 2:51 pm

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Source: Veritas Prep

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

The OA is A

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by Brent@GMATPrepNow » Tue Jan 08, 2019 3:15 pm
BTGmoderatorLU wrote:Source: Veritas Prep

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

The OA is A
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

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by GMATGuruNY » Tue Jan 08, 2019 3:41 pm
BTGmoderatorLU wrote:Source: Veritas Prep

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
When the SAME DISTANCE is traveled at two different speeds, the average speed for the entire trip will be CLOSER TO THE LOWER SPEED than to the higher speed.
The reason:
The portion traveled at the lower speed takes LONGER.
Since more time is spent at the lower speed than at the higher speed, the average speed for the entire trip will be closer to the lower speed.
Here, halfway between the two speeds = the average of the two speeds = (50+70)/2 = 60.
To be closer to the lower speed and to the higher speed, the average speed for the entire trip must be LESS THAN 60.

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by swerve » Wed Jan 09, 2019 9:37 am
For these type of questions we can apply direct formula given below:

2ab/(a+b), where a & b are avg. speed. So 2x50x70/(120)= 58.33 (approx).

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by Scott@TargetTestPrep » Mon Jan 21, 2019 5:58 pm
BTGmoderatorLU wrote:Source: Veritas Prep

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
We can use the following formula:

average rate = total distance/total time

If we let the distance each way = d, then the time to work = d/50, and the time from work = d/70. Thus:

average rate = 2d/(d/50 + d/70)

average rate = 2d/(7d/350 + 5d/350)

average rate = 2d/(12d/350)

average rate = (2d x 350)/12d

average rate = 350/6 = 58.3 mph

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