A driver completed the first 20 miles of a 40 miles trip at

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BTGmoderatorAT: Moderator; Posts: 426; Joined: Tue Aug 22, 2017 8:48 pm; Followed by:1 members

A driver completed the first 20 miles of a 40 miles trip at

by BTGmoderatorAT » Sun Dec 10, 2017 5:19 am

A driver completed the first 20 miles of a 40 miles trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-miles trip? ( Assume that the driver did not make any stops during the 40-miles trip)

A. 65
B. 68
C. 70
D. 75
E. 80

Is there a strategic approach to this question? Can any experts help?

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Source: Beat The GMAT — Problem Solving | Sun Dec 10, 2017 5:19 am

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by GMATGuruNY » Sun Dec 10, 2017 7:00 am

The question reads: A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? -assume that the driver did not make any stops during the 40 mile trip-

a. 65mph
b. 68mph
c. 70mph
d. 75mph
e. 80mph

Half the total distance is traveled at 50 miles per hour.
We can plug in ANY VALUE for the total distance, as long as half the total distance is traveled at 50 miles per hour.

Let the total distance = 300 miles.
Time to travel 300 miles at an average speed of 60 miles per hour = 300/60 = 5 hours.
Time to travel the first 150 miles at an average speed of 50 miles per hour = 150/50 = 3 hours.
Time remaining for the next 150 miles = total time - time for the first 150 miles = 5-3 = 2 hours.

To travel the next 150 miles in 2 hours, the required rate = 150/2 = 75 miles per hour.

The correct answer is D.

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by Brent@GMATPrepNow » Sun Dec 10, 2017 9:52 am

ardz24 wrote:A driver completed the first 20 miles of a 40 miles trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-miles trip? ( Assume that the driver did not make any stops during the 40-miles trip)

A. 65
B. 68
C. 70
D. 75
E. 80

Here's another approach:

The total distance is 40 miles, and we want the average speed to be 60 miles per hour.
Average speed = (total distance)/(total time)
So, we get: 60 = (40 miles)/(total time)
Solve equation to get: total time = 2/3 hours
So, the TIME for the ENTIRE 40-mile trip needs to be 2/3 hours.

driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour.
How much time was spent on this FIRST PART of the trip?
time = distance/speed
So, time = 20/50 = 2/5 hours

The ENTIRE trip needs to be 2/3 hours, and the FIRST PART of the trip took 2/5 hours

2/3 hours - 2/5 hours = 10/15 hours - 6/15 hours
= 4/15 hours
So, the SECOND PART of the trip needs to take 4/15 hours

The SECOND PART of the trip is 20 miles, and the time is 4/15 hours
Speed = distance/time
So, speed = 20/(4/15)
= (20)(15/4)
= 75

Answer: D

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Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by Scott@TargetTestPrep » Fri Sep 27, 2019 7:38 am

BTGmoderatorAT wrote:A driver completed the first 20 miles of a 40 miles trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-miles trip? ( Assume that the driver did not make any stops during the 40-miles trip)

A. 65
B. 68
C. 70
D. 75
E. 80

Is there a strategic approach to this question? Can any experts help?

We can use the following formula:

average rate = (distance 1 + distance 2)/(time 1 + time 2),

where average rate = 60, distance 1 = distance 2 = 20, time 1 = distance 1/rate 1 = 20/50 = 2/5, and time 2 = distance 2/rate 2 = 20/r (where r is the average speed of the remaining 20 miles).

Let's now determine r:

60 = (20 + 20)/(2/5 + 20/r)

60 = 40/(2r/5r + 100/5r)

60 = 40/[(2r + 100)/5r]

60 = 200r/(2r + 100)

60(2r + 100) = 200r

120r + 6000 = 200r

6000 = 80r

r = 6000/80 = 600/8 = 75

Alternate Solution:

In order to achieve an average speed of 60 mph, the driver must complete the entire journey in 40/60 = 2/3 hours. Note that he already spent 20/50 = 2/5 hours on the first 20 miles of the trip; thus, he must complete the remaining 20 miles in 2/3 - 2/5 = 4/15 hours. To travel 20 miles in 4/15 hours, his rate must be 20/(4/15) = (20 * 15)/4 = 5 * 15 = 75 mph.

Answer: D

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