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

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A car travels from point A to point B. The average speed of [#permalink]  26 Jul 2010, 21:46
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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
[Reveal] Spoiler: OA

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Re: distance problem [#permalink]  26 Jul 2010, 22:08
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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 $$60=\frac{180}{total \ time}$$ --> $$60=\frac{180x}{x+90}$$ --> $$60x+60*90=180x$$ --> $$120x=60*90$$ --> $$x=45$$.

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Re: A car travels from point A to point B. The average speed of [#permalink]  16 Nov 2012, 14:15
Thanks Bunuel!

An additional question: What is the logic behind picking numbers in this problem? , How do these numbers lead us to the answer?
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Re: A car travels from point A to point B. The average speed of [#permalink]  18 Nov 2012, 13:34
danzig wrote:
Thanks Bunuel!

An additional question: What is the logic behind picking numbers in this problem? , How do these numbers lead us to the answer?

180 is the least common multiple of 90 mi/hr and 60 mi/hr. Picking 180 makes calculations easy when you know d = rt
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Re: A car travels from point A to point B. The average speed of [#permalink]  27 Nov 2012, 02:28
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how about weighted average for this method? the number between 90 and 60 is 30. So it should be slightly higher than 30 and less than 60. So the ans is 45
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Re: A car travels from point A to point B. The average speed of [#permalink]  18 Aug 2013, 19:12
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Let distance be D. Half distance travelled at avg speed of 90m/h. Let x m/h be the avg speed for seconds half of the distance.
Given : Avg speed for the entire trip is 60

D/2/90 + D/2/x = D/60
D/180 + D/2x = D/60
Solving for x, we get 45m/h

Ans: B
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Re: A car travels from point A to point B. The average speed of [#permalink]  19 Aug 2013, 01:53
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average speed= 2 s1 s2/ s1+s2 (when disctance travelled is equal.)

i

2x 90 x s2
---------- = 60
90 + s2

180 s2 = 60 (90 + s2)

180s2- 60 s2 = 5400

s2 = 5400 / 120

s2 = 45
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Re: A car travels from point A to point B. The average speed of [#permalink]  13 Feb 2014, 06:05
1. Use 180 for each half distance, therefore total distance is 360
2. Total distance / Avg Speed = Total Time---> 360/60 = 60
3. Total time in first leg = 180/90 = 2 hrs
4. Avg speed in second leg= 180/4=45

B

Hope it helps
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J
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A car travels from point A to point B. The average speed of [#permalink]  26 Jun 2014, 02:27
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Let total distance = 2x
Avg Speed = 60

For first half
Distance = x
Speed = 90

For second Half
Distance =x
Speed = s (Assume)

Setting up the equation

$$\frac{x}{90} + \frac{x}{s} = \frac{2x}{60}$$

s = 45

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Re: A car travels from point A to point B. The average speed of [#permalink]  26 Jun 2014, 02:45
aiming4mba 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

VERY EASY USE THE FORMULA FOR EQUAL DISTANCE TRAVELLED OR HALF DISTANCE

AVERAGE SPEED = 2AB/A+B, WHERE A AND B ARE THE SPEEDS OF THE CAR IN FIRST HALF DISTANCE AND SECOND HALF DISTANCE RESP.

FOR THREE EQUAL DISTANCE USE AVG SPEED = 3ABC/A+B+C ==== SAME AS A,B,C ARE SPPED RESP

IN QUESTION A IS GIVEN FIND OUT B
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Re: A car travels from point A to point B. The average speed of [#permalink]  06 Sep 2014, 10:49
I am wondering... so "half the trip" refers to distance or to time? If "half the trip" means half of the distance, the answer is 45. If "half the trip" means half of the total time, the answer is 30.
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Re: A car travels from point A to point B. The average speed of [#permalink]  17 Sep 2014, 20:11
Avg. Speed = 2S1S2/(S1+S2),
we know S1 and we know Avg. Speed
So it is very easy to calculate S2
Ans. B
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Re: A car travels from point A to point B. The average speed of [#permalink]  03 Nov 2014, 12:12
FORMULA FOR CALCULATING AVERAGE SPEED =

Average speed = $$\frac{2 * S1 * S2}{S1+ S2}$$

let speed for 2nd part be X

$$60 =\frac{2 * 90 * X}{X + 90}$$

$$X + 90 = 3X$$

$$X = 45$$

P.S = If 3 speeds - A , B, C are given , then formula is = $$\frac{3 * A * B * C}{AB * AC * BC}$$

Please consider KUDOS if my post helped
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Re: A car travels from point A to point B. The average speed of [#permalink]  03 Nov 2014, 22:30
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vards wrote:
FORMULA FOR CALCULATING AVERAGE SPEED =

Average speed = $$\frac{2 * S1 * S2}{S1+ S2}$$

let speed for 2nd part be X

$$60 =\frac{2 * 90 * X}{X + 90}$$

$$X + 90 = 3X$$

$$X = 45$$

P.S = If 3 speeds - A , B, C are given , then formula is = $$\frac{3 * A * B * C}{AB * AC * BC}$$

Please consider KUDOS if my post helped

I don't think this formula would work always. It worked fine here because both the distances covered were in the ratio 1:1.

Case 1 : If a body travels from Point A to Point B with a speed of S1 and back from Point B to Point A with a speed of S2, then

$$Avg, Speed = 2*S1*S2 / (S1 + S2)$$

Case 2 : If a body covers part of a journey at speed S1 and remaining part of the journey at speed S2 and the distance covered are in the ratio D1:D2, then

$$Avg. Speed = (D1 + D2)*S1*S2 / (D1*S2 + D2*S1)$$

Had the distances been covered in ratios other than 1:1, then Case 1 would not give the right answer. We would have to use Case 2 then.

Please correct me if I'm wrong.
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Re: A car travels from point A to point B. The average speed of [#permalink]  03 Nov 2014, 22:38
siggarusfigs wrote:
I am wondering... so "half the trip" refers to distance or to time? If "half the trip" means half of the distance, the answer is 45. If "half the trip" means half of the total time, the answer is 30.

Half the trip refers the distance
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A car travels from point A to point B. The average speed of [#permalink]  04 Nov 2014, 00:05
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Ashishmathew01081987 wrote:
vards wrote:
FORMULA FOR CALCULATING AVERAGE SPEED =

Average speed = $$\frac{2 * S1 * S2}{S1+ S2}$$

let speed for 2nd part be X

$$60 =\frac{2 * 90 * X}{X + 90}$$

$$X + 90 = 3X$$

$$X = 45$$

P.S = If 3 speeds - A , B, C are given , then formula is = $$\frac{3 * A * B * C}{AB * AC * BC}$$

Please consider KUDOS if my post helped

I don't think this formula would work always. It worked fine here because both the distances covered were in the ratio 1:1.

Case 1 : If a body travels from Point A to Point B with a speed of S1 and back from Point B to Point A with a speed of S2, then

$$Avg, Speed = 2*S1*S2 / (S1 + S2)$$

Case 2 : If a body covers part of a journey at speed S1 and remaining part of the journey at speed S2 and the distance covered are in the ratio D1:D2, then

$$Avg. Speed = (D1 + D2)*S1*S2 / (D1*S2 + D2*S1)$$

Had the distances been covered in ratios other than 1:1, then Case 1 would not give the right answer. We would have to use Case 2 then.

Please correct me if I'm wrong.

Yes u r absolutely correct. I couldnt write the details of formula as comprehensively as u did. If equal distances are covered are covered at different speeds , then the formula for 2 speeds and 3 speeds applies as written in my post. If different distances are travelled , then the Case 2 in your post applies. +1 kudos to u
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Re: A car travels from point A to point B. The average speed of [#permalink]  09 Feb 2015, 06:27
aiming4mba 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

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Re: A car travels from point A to point B. The average speed of [#permalink]  10 Feb 2015, 09:46
PareshGmat wrote:
Let total distance = 2x
Avg Speed = 60

For first half
Distance = x
Speed = 90

For second Half
Distance =x
Speed = s (Assume)

Setting up the equation

$$\frac{x}{90} + \frac{x}{s} = \frac{2x}{60}$$

s = 45

Hello,
could you kindly provide the steps of the equation to the solution s = 45 ?
Re: A car travels from point A to point B. The average speed of   [#permalink] 10 Feb 2015, 09:46
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