A train moves from P to Q at an average speed of 90km/h and immediately returns from Q to P through the same route at an average speed of 45km/h. Find the average speed for the entire journey
A
55.00km/h
B
60.00km/h
C
67.50km\h
D
75.00km\h
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Let the distance from P to Q = d km
(We don't need the actual value of d — it will cancel out.)
Time taken from P to Q = \(\frac{\text{d}}{90}\) hours
Time taken from Q to P = \(\frac{\text{d}}{45}\) hours
Total distance travelled = d + d = 2d km
Total time taken = \(\frac{\text{d}}{90}\) + \(\frac{\text{d}}{45}\)
= \(\frac{\text{d}}{90}\) + \(\frac{2d}{90}\) = \(\frac{3d}{90}\)
= \(\frac{\text{d}}{30}\) hours
Average speed = \(\frac{\text{total distance}}{\text{total time}}\)
= 2d \div (\(\frac{\text{d}}{30}\)) = 2d \times (\(\frac{30}{\text{d}}\)) = 60 km/h
Source: Myschool Past Questions Archive (Record #31804)