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Too complicated to solve

by [email protected] » Mon Jul 08, 2013 9:05 pm
A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

Choices

A 30

B 45
C 60


D 75
E It cannot be determined from the information given.

Can we back solve this question?
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by Brent@GMATPrepNow » Mon Jul 08, 2013 10:08 pm
[email protected] wrote:A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

Choices

A 30

B 45
C 60


D 75
E It cannot be determined from the information given.
I'm assuming that we're saying that half of the distance is driven at 90 miles per hour, and the other half is driven at a different speed.

Average speed = (total distance)/(total time)

Total distance
Let d = distance traveled during first half of the trip at a speed of 90 mph
Let d = distance traveled during second half of the trip at a speed of x mph
So, the total distance traveled = 2d


Total time
To calculate the total time, we must find the time required for the first half of the trip and the time required for the second half of the trip

Time required for the first half of the trip (at 90 mph)
Time = distance/speed
So, time = d/90

Time required for the second half of the trip (at x mph)
Time = distance/speed
So, time = d/x

So, total time = d/90 + d/x
= dx/90x + 90d/90x [found common denominator]
= (dx + 90d)/90x


Average speed = (total distance)/(total time)
= 2d/(dx + 90d)/90x
= (2d)[90x/(dx + 90d)]
= 180dx/(dx + 90d)
= 180x/(x + 90)

The average speed if the entire trip is 60 miles per hour.
So, 180x/(x + 90) = 60
Cross multiply to get: 180x = 60(x + 90)
Expand: 180x = 60x + 5400
Simplify: 120x = 5400
Solve: x = 45
Answer: B

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by GMATGuruNY » Tue Jul 09, 2013 2:26 am
[email protected] wrote:A car travels from point A to point B. The average speed of the car is 60 miles/hr and it travels the first half of the trip at a speed of 90 mi/hr. What is the speed of the car in the second half of the trip?

A 30
B 45
C 60
D 75
E It cannot be determined from the information given.
Let the total distance = 180 miles.
Time to travel the entire 180 miles at an average speed of 60 miles per hour = d/r = 180/60 = 3 hours.
Time to travel the first 90 miles at 90 miles per hour = d/r = 90/90 = 1 hour.
Thus, the time to travel the second 90 miles = 3-1 = 2 hours.
Speed for the second 90 miles = d/t = 90/2 = 45 miles per hour.

The correct answer is B.

An alternate approach is to plug in the answers, which represent the speed for the second half of the trip.

Speed for the first half of the trip = 90 miles per hour.
Average speed for the whole trip = 60 miles per hour.
Since the speed for the first half of the trip is GREATER than the average speed for the whole trip, the speed for the second half of the trip must be LESS than the average speed for the whole trip.
Eliminate C, D and E.

Answer choice A: 30 miles per hour
It will take LONGER to travel the second half of the trip at 30 miles per hour than it takes to travel the first half of the trip at 90 miles per hour.
Since more time will be spent traveling at the slower speed, the average speed for the entire trip will be closer to the slower speed (30) than to the faster speed (90).
The result is that the average speed for the whole trip will be LESS than 60 miles per hour (halfway between 30 and 90).
Eliminate A.

The correct answer is B.
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