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

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: \(total \ time=\frac{x}{80}+\frac{x}{24}+\frac{x}{48}=\frac{18x}{240}\);

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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)

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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

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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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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

gmatclubot

Re: If a car went the first third of the distance at 80 kmh, the &nbs
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26 Oct 2018, 01:33