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Math Expert V
Joined: 02 Sep 2009
Posts: 64150

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Difficulty:   55% (hard)

Question Stats: 69% (02:09) correct 31% (01:42) wrong based on 84 sessions

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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

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Math Expert V
Joined: 02 Sep 2009
Posts: 64150

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Official Solution:

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

Say the total distance is $$3x$$ kilometers, then: $$total \ time=\frac{x}{80}+\frac{x}{24}+\frac{x}{48}=\frac{18x}{240}$$;

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

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##### General Discussion
Intern  B
Joined: 15 Feb 2018
Posts: 1

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I think this is a high quality question, thanks
Intern  S
Status: Current Student
Joined: 26 Mar 2014
Posts: 26
Concentration: Entrepreneurship, Finance

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1
$$Rate*time=distance$$
So, $$80*t=\frac{1}{3} => t1=\frac{1}{3}*80$$
Similarly, $$t2=\frac{1}{3}*24$$ and $$t3=\frac{1}{3}*48$$
So, total time= $$t1+t2+t3 = \frac{1}{3}(\frac{1}{80}+\frac{1}{24}+\frac{1}{48}) = \frac{1}{3}*\frac{1}{8}(\frac{1}{10}+\frac{1}{3}+\frac{1}{6}) = \frac{1}{24}*\frac{18}{30} = \frac{1}{40}$$
Average speed = $$\frac{(total distance)}{(total time)}= \frac{1}{1/40}$$ = 40 kph M15-32   [#permalink] 24 Feb 2018, 17:41

# M15-32

Moderators: chetan2u, Bunuel  