If a car traveled the first third of the distance at 80 km/h, the

Question

If a car traveled the first third of the distance at 80 km/h, the second third at 24 km/h, and the final third at 48 km/h, what was the car's average (arithmetic mean) speed for the entire journey?

A. 36 km/h
B. 40 km/h
C. 42 km/h
D. 44 km/h
E. 50 km/h

M15-32

Bunuel · Accepted Answer

If a car traveled the first third of the distance at 80 km/h, the second third at 24 km/h, and the final third at 48 km/h, what was the car's average (arithmetic mean) speed for the entire journey?

A. 36 km/h
B. 40 km/h
C. 42 km/h
D. 44 km/h
E. 50 km/h

Let the total distance be  3x  kilometers. Then, the total time taken is given by  \frac{x}{80} + \frac{x}{24} + \frac{x}{48} = \frac{18x}{240}  hours.
 
The average speed is calculated as  \frac{total \ distance}{total \ time} . Thus, average speed  = \frac{3x}{\frac{18x}{240}} = \frac{240*3}{18} = 40  km/h.
 
Answer: B.

nyknicks4412 · Answer

I don't know if I got lucky with smart numbers but....

Average Speed = \frac{Total Distance}{Total Time}

Set total distance: 30

That means each third had a distance of 10.

Calculate time for each third and sum them to get total time:  \frac{10}{80} + \frac{10}{24} + \frac{10}{48} = \frac{3}{4}

Back to the original equation...

Average Speed = \frac{30}{3/4}  which simplifies to  \frac{30 * 4}{3}  = 40

BrentGMATPrepNow · Answer

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    
= 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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ScottTargetTestPrep · Answer

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

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

chetan2u · Answer

Such questions are best done by taking smart numbers, because whatever be the distance the answer will remain the same.

What can be a smart number here. It has to be something to do with the LCM of three speeds.
LCM(80,24,48) = 240.
So you can take each  \frac{1}{3}^{rd}  portion as 240 or 480.

Let us take the distance for each part as 480.

A car went the first third of the distance at 80 kmh, so time taken =>  \frac{480}{80}=6 
The second third at 24 kmh, so time taken =>  \frac{480}{24}=20 
The last third at 48 kmh, so time taken =>  \frac{480}{48}= 10

Total time =  6+20+10=36   
Distance = 3*480

The average speed of the car for the entire trip =  \frac{3*480}{36}=40 kmph

B

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If a car traveled the first third of the distance at 80 km/h, the

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