Question

On a 120 km long track, a train travels the first 30 km with a uniform speed of 30 km/h. How fast must the train travel for the rest part of the journey so as to average 60 km/h for the entire trip?

• A. 90 km/h
• B. 80 km/h
• C. 70 km/h
• D. 60 km/h

Answer 1

The correct option is (A) 90 km/h

Step 1, Given data

Total distance = 120 km

30 km with a speed 30 km/h

Average speed = 60 km/h

Step 2, Finding the speed

Average speed for entire journey = 60 km/h

So, total time to be taken for the entire journey, T$=\frac{120km}{60{kmh}^{-1}}=2h$

Now, time taken during first half of journey, $t=\frac{60km}{60km{h}^{-1}}=1h$

Time taken for second half of journey = $\text{T - t = 2 h - 1 h = 1 h}$

Distance covered in second part of journey = Total distance - Distance covered in first part of journey $\text{= 120 km - 30 km = 90 km}$

Hence, average speed for second half =$\frac{90km}{1h}=90{kmh}^{-1}$