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\(Rate*time=distance\)
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
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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
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I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.
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when distance is same for all 3 parts then why cant i just divide by 3

like 24+48+80/3
Bunuel
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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
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when distance is same for all 3 parts then why cant i just divide by 3

like 24+48+80/3
Bunuel
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

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.
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