An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 km/h, respectively. What is the average speed in km/h for the entire journey?
72
73
74
75
ANSWER
The average speed for the whole round trip is 72 km/h, which is option (A).
Official answer: ASource: Official answer key, GATE 2018 IN (IIT Guwahati)
Let the one-way distance from A to B be . The car covers that distance twice, so the total distance is .
Time is distance divided by speed. Onward time h and return time h.
Total time h.
Average speed is total distance divided by total time:
Check with the equal-distance shortcut (the harmonic mean of the two speeds):
72 km/h is option (A).
KEY IDEA
Average speed means total distance divided by total time. When two legs cover the same distance at speeds and , the average is their harmonic mean, . The car spends longer on the slower leg, so that speed counts for more.
WATCH OUT FOR
Taking the arithmetic mean of the two speeds, km/h, and picking option (D). That would only be right if the car spent equal TIME at each speed. Here it covers equal DISTANCES, so it spends 1.5 times as long at 60 km/h as at 90 km/h, and the true average falls below 75.
From the GATE 2018 IN paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes
