During a journey of 200 km, the average speed of a car is 125 km/h. But if for the first 100 km, the driver increases its earlier average speed by 20% and then decreases it to its (2/3)rd for next 100 km. What will be the new average speed?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 120 km/h
Average speed is the total distance divided by the total time, not the average of the two speeds. The car spends longer on the slower half, so the slower speed counts for more.
The two new speeds:
First 100 km: 125 km/h increased by 20%, \(125\times1.2=150\) km/h
Next 100 km: \(\frac{2}{3}\) of that speed, \(\frac{2}{3}\times150=100\) km/h
The times:
First 100 km: \(\displaystyle \frac{100}{150}=\frac{2}{3}\) h
Next 100 km: \(\displaystyle \frac{100}{100}=1\) h
Total time \(\displaystyle =\frac{2}{3}+1=\frac{5}{3}\) h
The new average speed:
\(\displaystyle 200\div\frac{5}{3}=120\) km/h
Shortcut: For two equal distances covered at speeds \(a\) and \(b\), the average speed is \(\displaystyle\frac{2ab}{a+b}\).
\(\displaystyle \frac{2\times150\times100}{150+100}=\frac{30000}{250}=120\) km/h