Time, Speed and Distance
Time-speed-distance questions reward unit discipline above all else — most wrong answers come from mixing km/h and m/s rather than from a flawed method.
10 questions · 5 minutes · instant scoring
What this topic actually tests
The core relationship, Distance = Speed x Time, underlies every question in this topic, and the fastest CLAT technique is converting units early so you never have to convert mid-calculation. To convert km/h to m/s, multiply by 5/18; to convert m/s to km/h, multiply by 18/5 — memorising these two conversion factors, rather than deriving them each time, saves valuable seconds. For two bodies moving toward each other, use relative speed = sum of individual speeds; for two bodies moving in the same direction, use relative speed = difference of individual speeds — this single idea covers trains crossing each other, people walking toward or away from one another, and boats moving with or against a stream. For a train crossing a stationary object (a pole or a person), the distance covered equals the train's own length; for a train crossing an extended object like a platform or bridge, the distance covered equals the train's length plus the object's length — this length-addition is the most commonly tested variant. For boats and streams, downstream speed = boat speed + stream speed, and upstream speed = boat speed - stream speed; given both downstream and upstream speeds, boat speed in still water = their average, and stream speed = half their difference. Worked example: a train running at 72 km/h (= 20 m/s) crosses a platform 250 m long in 30 seconds. Total distance covered = speed x time = 20 x 30 = 600 m, and since this distance equals the train's length plus the platform's length, the train's length = 600 - 250 = 350 m. For average speed over two equal distances at different speeds, never average the two speeds directly — use the harmonic-mean formula 2ab/(a+b), since more time is spent at the slower speed.
The common trap on this topic
The most common trap in this topic is averaging two speeds arithmetically when a journey covers equal distances at different speeds — for example, assuming a return trip at 60 km/h one way and 40 km/h the other way gives an average speed of 50 km/h. This is wrong because the traveler spends more time at the slower speed, so the correct average speed is the harmonic mean, 2 x 60 x 40/(60+40) = 48 km/h, always lower than the simple arithmetic average whenever the two speeds differ. A second frequent trap is forgetting to add the length of the train itself when it crosses a platform, bridge, or another train, using only the platform's or bridge's length as the distance covered — the correct distance is always the sum of both lengths. A third trap, specific to boats-and-streams and 'walking at a fraction of usual speed' questions, is confusing which of the two given speeds (or the ratio of speeds) corresponds to time saved versus time lost; because time is inversely proportional to speed for a fixed distance, a decrease in speed always corresponds to an increase in time, and setting up this inverse relationship incorrectly is a common source of sign errors.
Take the micro-test
A car travels 180 km in 3 hours. Find its speed in metres per second.
A train 150 m long crosses a pole in 15 seconds. Find its speed in km/h.
Two trains, 120 m and 180 m long, run in opposite directions on parallel tracks at 54 km/h and 36 km/h respectively. Find the time they take to completely cross each other.
Find the total time taken for the entire 300 km journey.
Find his average speed for the entire 300 km journey.
A boat's speed in still water is 15 km/h and the speed of the stream is 5 km/h. Find the time taken by the boat to travel 80 km downstream.
A man rows upstream at 6 km/h and downstream at 10 km/h. Find his speed in still water.
A and B are 60 km apart. They start walking towards each other at the same time, at speeds of 8 km/h and 12 km/h respectively. After how long will they meet?
A train running at 72 km/h crosses a platform 250 m long in 30 seconds. Find the length of the train.
A car covers a certain distance at 60 km/h and returns over the same distance at 40 km/h. Find its average speed for the entire round trip.
FAQ
What are the key unit conversions I should memorise for CLAT time-speed-distance questions?
To go from km/h to m/s, multiply by 5/18; to go from m/s to km/h, multiply by 18/5. Doing this conversion once at the start of a question, rather than partway through, avoids most careless errors on this topic.
When should I use relative speed, and is it a sum or a difference?
Use the sum of speeds when two bodies move toward each other (or in opposite directions) and the difference of speeds when they move in the same direction — this applies to trains, boats, and people walking or running.
Can I just average two speeds to find average speed over a round trip?
Only if the time spent at each speed is equal. If the distances (not the times) are equal, as in most CLAT questions, you must use the formula 2ab/(a+b), which always gives a value lower than the simple arithmetic average.
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