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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On a certain Monday, Carlos drove to work at an average
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BTGmoderatorLU
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Average speed = (TOTAL distance)/TOTAL travel time)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
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
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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.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 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.
The correct answer is A.
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We can use the following formula: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
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
Answer: A
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