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If a car went the first third of the distance at 80 kmh, the

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If a car went the first third of the distance at 80 kmh, the  [#permalink]

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New post 05 Oct 2010, 11:20
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If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

A. 36 kmh
B. 40 kmh
C. 42 kmh
D. 44 kmh
E. 50 kmh

(C) 2008 GMAT Club - m15#32
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Re: GMAT club Test m15#32  [#permalink]

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New post 05 Oct 2010, 11:41
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AndreG wrote:
If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

(C) 2008 GMAT Club - m15#32

* 36 kmh
* 40 kmh
* 42 kmh
* 44 kmh
* 50 kmh


\(Average \ speed=\frac{total \ distance}{total \ time}\), let the total distance be \(3x\), then: \(total \ time=\frac{x}{80}+\frac{x}{24}+\frac{x}{48}=\frac{18x}{240}\);

\(Average \ speed=\frac{total \ distance}{total \ time}=\frac{3x}{\frac{18x}{240}}=\frac{240*3}{18}=40\).

Answer: B.
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Re: GMAT club Test m15#32  [#permalink]

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New post 05 Oct 2010, 11:44
Thanks! I confused distance with time and just couldnt wrap my head around where I went wrong ;)
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Re: If a car went the first third of the distance at 80 kmh, the  [#permalink]

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New post 27 Jan 2015, 19:33
If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

A. 36 kmh
B. 40 kmh
C. 42 kmh
D. 44 kmh
E. 50 kmh


SOLUTION:

Assume D/3 = 240 (this number is convenient because it is divisible by 80, 24 and 48)

So:
240 = 80*T1 = 3 hrs
240 = 24*T2 = 10 hrs
240 = 48*T3 = 5 hrs

T = T1 + T2 + T3 = 18 hrs

D = RT
(240*3) = R*18
R = 40

ANSWER: B
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Re: If a car went the first third of the distance at 80 kmh, the  [#permalink]

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New post 06 May 2018, 12:01
Top Contributor
AndreG wrote:
If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

A. 36 kmh
B. 40 kmh
C. 42 kmh
D. 44 kmh
E. 50 kmh


Here's an algebraic approach:

Let d = 1/3 of the total distance traveled
So, the car traveled d km at 80 kmh, then the car traveled d km at 24 kmh, and then d km at 48 kmh

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

Total distance traveled = d + d + d = 3d

time = distance/speed
Total time spent traveling = (time spent traveling 80kmh) + (time spent traveling 24 kmh) + (time spent traveling 48 kmh)
= d/80 + d/24 + d/48 [let's rewrite this with a common denominator]
= 3d/240 + 10d/240 + 5d/240
= 18d/240
= 9d/120
= 3d/40

Average speed = (3d)/(3d/40)
= 120d/3d
= 40

Answer: B

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Re: If a car went the first third of the distance at 80 kmh, the  [#permalink]

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New post 08 May 2018, 10:35
AndreG wrote:
If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

A. 36 kmh
B. 40 kmh
C. 42 kmh
D. 44 kmh
E. 50 kmh


We can let the total distance = 3d and create the equation:

average = 3d/(d/80 + d/24 + d/48)

average = 3d/(d/80 + d/24 + d/48)

average = 3d/(3d/240 + 10d/240 + 5d/240)

average = 3d/(18d/240)

average = 720d/18d = 40

Answer: B
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Re: If a car went the first third of the distance at 80 kmh, the  [#permalink]

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New post 22 May 2018, 03:08
One can use simple formula when same distance is covered T different speed

a,b,c are different speed covering same distance

Av speed=3abc/(ab+bc+ac)

=3*80*24*48/(80*24+24*48+80*48)

=40

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If a car went the first third of the distance at 80 kmh, the  [#permalink]

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New post Updated on: 26 Oct 2018, 08:28
Let the distance travelled by each be "x"
Distance travelled by all= 3x.

Time taken by all= x/80+x/24+x/48
Average speed= Total distance/Total time= 3x/(x/80+x/24+x/48)=> 40 mph
Average speed= 40 mph

Ans(B)

Originally posted by jalice on 20 Oct 2018, 06:48.
Last edited by jalice on 26 Oct 2018, 08:28, edited 2 times in total.
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Re: If a car went the first third of the distance at 80 kmh, the  [#permalink]

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New post 26 Oct 2018, 01:33
Solved by picking a smart number:

Let R be the rate, D the distance, and T the time.

We want to know the average R, which is calculated as follows: \(\frac{Total D}{Total T}\).

1. Let us pick a smart number for the total D. D=120. Thus, every third of the total D = 40.
2. Let us now find the time travelled for every third of the total D:\(\frac{40}{80}\), \(\frac{40}{24}\), and \(\frac{40}{48}\), which reduces to \(\frac{1}{2}\),\(\frac{5}{3}\), and \(\frac{5}{6}\).
3. In order to get total T, we have to sum the individual Ts for the 3 thirds up: \(\frac{3}{6}+\frac{10}{6}+\frac{5}{6}=\frac{18}{6}=3\). Hence the total T = 3 hrs.
4. Now we have all the required components, total D and total T, to compute our average R: \(\frac{120}{3}=40\).

Please hit Kudos if you liked this approach :)
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Re: If a car went the first third of the distance at 80 kmh, the &nbs [#permalink] 26 Oct 2018, 01:33
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