M15-32

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

Bunuel · Accepted Answer

Official Solution:

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

Aks111 · Answer

Instead of using fractions to compute, one can use LCM as the total distance.
Let, Distance travelled in each 1/3rd part = 240 km
Total Distance = 240 * 3 km
Time taken when travelling at 80 kmh = 240 / 80 = 3 hr
Time taken when travelling at 24 kmh = 240 / 24 = 10 hr
Time taken when travelling at 48 kmh = 240 / 48 = 5 hr

Hence, average speed for entire trip = Total Distance / Total time taken = 240 *3 / (3+10+5) = 240 *3 / 18 = 40 kmh

Answer: B

rolings · Answer

I think this is a  high quality  question, thanks

zmtalha · Answer

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

Bunuel · Answer

I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.

rak08 · Answer

when distance is same for all 3 parts then why cant i just divide by 3

like 24+48+80/3

Bunuel · Answer

You can’t just average the speeds as (80 + 24 + 48)/3 because average speed is not the arithmetic mean when time or speed varies. The car spends different amounts of time at each speed, so you need to use the formula:

Average speed = total distance / total time

That’s why dividing by 3 doesn’t work here.

renanreis · Answer

I like the solution - it’s helpful.

sb995 · Answer

I did not quite understand the solution. Do you have any suggestions on how to eyeball the solution for this instead of using algebra? Thank you.

Bunuel · Answer

The official solution is actually very simple and just uses the basic principle: average speed = total distance / total time.

We let the total distance be 3x (so each part is x).

Then we add the times: x/80 + x/24 + x/48. That sum simplifies to 18x/240.

Finally, divide total distance (3x) by that total time (18x/240) to get 40.

That’s all. Once you see it, it comes very easily.

JuDC · Answer

I like the solution - it’s helpful.

Gc2kawai · Answer

I like the solution - it’s helpful.

tanishapriya96 · Answer

this was helpful, thanks!

icandoit4u · Answer

I like the solution - it’s helpful.

eaexpedita · Answer

I like the solution - it’s helpful.

M15-32

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