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In a 40-mile trip, the first 20 miles were traveled in

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by M7MBA » Thu Mar 22, 2018 5:22 am
In a 40-mile trip, the first 20 miles were traveled in 50mph. If the total trip average speed is 60mph, what should be the average speed in the last 20 miles?

A) 150
B) 75
C) 50
D) 45
E) 40

The OA is the option B.

What are the equations that are needed here? Can any expert bring me an explanation here? Thanks in advanced.
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In a 40-mile trip, the first 20 miles were traveled in

by Brent@GMATPrepNow » Thu Mar 22, 2018 8:01 am
M7MBA wrote:In a 40-mile trip, the first 20 miles were traveled in 50mph. If the total trip average speed is 60mph, what should be the average speed in the last 20 miles?

A) 150
B) 75
C) 50
D) 45
E) 40
Here's one 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.

The 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 mph

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by elias.latour.apex » Thu Mar 22, 2018 7:03 pm
The question is easily solvable while doing hardly any math at all.

If the first half of the trip was completed at 50 mph and the second half of the trip were completed at 50 mph or less, then the average would never exceed 50 mph. Thus, choices C, D, and E can be eliminated.

Choices A and B are so widely spread that it is obvious that (B) is the best answer. Why, therefore, would anyone break down and start doing calculations designed to determine the total time of the trip, then the time spent on the first leg so as to calculate the time spent on the second leg? This is a waste of time and mental energy that could best be used on a different problem that actually requires such an expenditure.

Don't use a four-step math procedure on a problem that doesn't need it.
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by Jeff@TargetTestPrep » Fri Mar 23, 2018 11:51 am
M7MBA wrote:In a 40-mile trip, the first 20 miles were traveled in 50mph. If the total trip average speed is 60mph, what should be the average speed in the last 20 miles?

A) 150
B) 75
C) 50
D) 45
E) 40
We can see that the time for the first 20 miles of the trip is 20/50 = 2/5 of an hour. We can let the rate of the second 20 miles of the trip be r, so that the time for the second 20 miles is 20/r. We can create the equation:

60 = 40/(2/5 + 20/r)

60(2/5 + 20/r) = 40

24 + 1200/r = 40

1200/r = 16

1200 = 16r

75 = r

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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