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A car travels from point A to point B. The average speed

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A car travels from point A to point B. The average speed [#permalink] New post 18 Jun 2011, 03:32
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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. 90

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-car-travels-from-point-a-to-point-b-the-average-speed-of-98076.html
[Reveal] Spoiler: OA
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Re: Speed P.S Problem [#permalink] New post 18 Jun 2011, 04:19
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Avg Speed = Total Distance / Total time.

Let total distance = d
Let the speed of the car in the second half of the trip = S
Time taken to travel first half (d/2) at speed of 90m/hr t1= d/2*90 = d/180
Time taken to travel second half (d/2) at speed of s m/hr t2= d/2*s = d/2s

Total time = t1+t2 = d/180 + d/2s

Avg Speed = Total Distance / Total time.
60 = d/(t1+t2)
60=d/[(d/180) + d/2s)]
60 = 360s/(2s+180)
s=45

OA B.
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Re: Speed P.S Problem [#permalink] New post 18 Jun 2011, 05:18
guygmat 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)90


By weighted average:

Let the speed be S;

\frac{\frac{1}{S}-\frac{1}{60}}{\frac{1}{60}-\frac{1}{90}}=\frac{x}{x}=1

Upon solving;
S=45 m/h

Ans: "B"
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Re: Speed P.S Problem [#permalink] New post 18 Jun 2011, 07:11
guygmat 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)90


Avg speed formula = 2XY/(x+Y)

2X*90/x+90 = 60
180X= 60X+5400
120X= 5400
X= 45.
B
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Re: Speed P.S Problem [#permalink] New post 23 May 2013, 06:56
Great explanations this question was really tricky!
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Re: A car travels from point A to point B. The average speed [#permalink] New post 23 May 2013, 08:29
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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. 90

Let the average speed for the second half of the trip be x miles per hour.

Pick some smart number for the distance from A to B: let the distance be 180 miles, so half of the distance will be 90 miles.

Average \ speed=\frac{total \ distance}{total \ time} --> 60=\frac{180}{total \ time};

Total time equals time for the first half plus time for the second half --> \frac{90}{90}+\frac{90}{x}=\frac{x+90}{x};

So 60=\frac{180}{total \ time} --> 60=\frac{180x}{x+90} --> 60x+60*90=180x --> 120x=60*90 --> x=45.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-car-travels-from-point-a-to-point-b-the-average-speed-of-98076.html
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Re: A car travels from point A to point B. The average speed   [#permalink] 23 May 2013, 08:29
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