rak08
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.