distance and time

Jun 17, 2025

Updated 13 hours ago

6 min read

Distance, Time and Speed Problems for Placement Exams

Speed, distance, and time problems show up in almost every competitive exam and campus placement test. The math itself isn't hard — the formulas are simple. What trips people up is the unit conversions, the relative speed logic, and the boat-stream twist. Once you understand those three things clearly, this entire topic becomes manageable.

This article covers the core concepts and then walks through 22 practice problems — with answers and solving hints for each.

The Core Formulas You Need

D i s t an ce = S p ee d \times T im e

S p ee d = \frac{D i s t an ce}{T im e}

T im e = \frac{D i s t an ce}{S p ee d}

Unit conversion (the one people forget most):

To convert km/h to m/s → multiply by $\frac{5}{18}$

To convert m/s to km/h → multiply by $\frac{18}{5}$

Relative speed:

Same direction → subtract the speeds
Opposite direction → add the speeds

Boat and stream:

Downstream speed =

boatspeed + streamspeed

Upstream speed =

boatspeed - streamspeed

Stream speed =

\frac{( downstream - upstream )}{2}

Boat speed in still water =

\frac{( downstream + upstream )}{2}

Keep these on a sticky note while practicing. You'll internalize them fast.

Part 1: Problems

Q1. A 160-meter-long train crosses a 160-meter-long platform in 16 seconds. What is the speed of the train?

Hint: Total distance covered = length of train + length of platform. Speed = total distance ÷ time. Convert to km/h by multiplying by 18/5.

✅ 72 km/h

Q2. A train with constant speed passes a 70-meter platform in 12 seconds and a 120-meter platform in 15 seconds. Find the length and speed of the train.

Hint: Set up two equations using (train length + platform length) ÷ time = speed. Since speed is constant, equate both expressions and solve for train length first.

✅ Length = 130 m, Speed = 60 km/h

Q3. A 220-meter-long train is running at 39 km/h. In how much time will it pass a pole completely?

Hint: Convert speed to m/s. Time = distance ÷ speed. Distance here is just the train's own length — a pole has no width.

✅ ~20.3 seconds

Q4. A man's speed with the current is 15 km/h and the speed of the current is 2.5 km/h. What is his speed against the current?

Hint: Speed with current = still water speed + stream speed. Find still water speed first, then subtract stream speed for upstream.

✅ 10 km/h

Q5. A man rows at 6 km/h in still water. Upstream takes twice as long as downstream. Find the rate of the stream.

Hint: Same distance both ways. If downstream time = t, upstream time = 2t. Write distance = speed × time for both and equate.

✅ 2 km/h

Q6. A man rows at 7.5 km/h in still water. Current is 1.5 km/h. He takes 50 minutes to row to a place and back. How far is his destination?

Hint: Total time = d/downstream + d/upstream = 50/60 hours. Downstream = 9 km/h, upstream = 6 km/h. Solve for d.

✅ 3 km

Q7. Walking at 3/4 of his usual speed, a man reaches 20 minutes late. What is his usual time?

Hint: At 3/4 speed, time becomes 4/3 of usual. Extra time = 4t/3 − t = t/3. Set t/3 = 20 and solve.

✅ 60 minutes

Q8. A train travels at 30 km/h for 12 minutes then at 45 km/h for 8 minutes. What is the average speed?

Hint: Average speed = total distance ÷ total time. Calculate each distance separately — don't just average the two speeds.

✅ 36 km/h

Q9. A and B ride from Delhi to Meerut (60 km). B's speed is 8 km/h, A is 4 km/h slower. When A is 12 km from Meerut he turns back and meets B. Find A's speed.

Hint: A's speed = B's speed − 4. The meeting condition in the question confirms the scenario.

✅ 4 km/h

Q10. A and B walk around a circular track in opposite directions, doing 3 and 5 rounds/hr respectively. Starting at 8 AM, how many times do they cross before 9:30 AM?

Hint: Opposite directions → relative speed = sum of speeds. Crossings = relative speed × total time.

✅ 12 times

Part 2: Problems

Q11. A train 132 m long passes a telegraph pole in 6 seconds. What is the speed of the train?

Hint: Passing a pole means the train travels its own length. Speed = 132 ÷ 6 m/s, then convert to km/h.

✅ 79.2 km/h

Q12. A train at 60 km/h crosses a 200-meter platform in 27 seconds. Find the length of the train.

Hint: Convert speed to m/s. Total distance = speed × time = train length + platform length.

✅ 250 meters

Q13. A 150-meter train crosses a 500-meter bridge in 30 seconds. How long to cross a 370-meter platform?

Hint: Find speed from the first scenario, then apply it to the new total distance (train + platform).

✅ 24 seconds

Q14. A 110-meter train at 60 km/h passes a man running at 6 km/h in the opposite direction. Time to pass?

Hint: Opposite directions → relative speed = 60 + 6 = 66 km/h. Convert to m/s, then time = length ÷ relative speed.

✅ 6 seconds

Q15. Two equal-length trains, same direction, at 46 km/h and 36 km/h. Faster passes slower in 36 seconds. Find each train's length.

Hint: Same direction → relative speed = 46 − 36 = 10 km/h. Distance covered = 2 × train length.

✅ 50 meters each

Q16. A man rows 32 km downstream and 14 km upstream, each taking 6 hours. Find the velocity of the current.

Hint: Downstream speed = 32/6, upstream = 14/6. Stream speed = (downstream − upstream) ÷ 2.

✅ 1.5 km/h

Q17. A boat travels 7 km upstream in 42 minutes. Stream speed is 3 km/h. Find boat speed in still water.

Hint: Upstream speed = distance ÷ time (convert minutes to hours). Still water speed = upstream speed + stream speed.

✅ 13 km/h

Q18. Boat speed in still water = 10 km/h. Travels 26 km downstream and 14 km upstream in equal time. Find stream speed.

Hint: Equal time means 26/(10 + s) = 14/(10 − s). Cross multiply and solve for s.

✅ 3 km/h

Q19. Man rows at 5 km/h in still water. Current = 1 km/h. Takes 1 hour to row to a place and back. How far?

Hint: d/downstream + d/upstream = 1 hour. Downstream = 6, upstream = 4. Solve for d.

✅ 2.4 km

Q20. A goods train leaves a station. After 6 hours, an express at 90 km/h leaves and catches up in 4 hours. Find goods train speed.

Hint: Both cover the same distance. Goods train runs for 10 hours total, express for 4 hours. Equate distances.

✅ 36 km/h

Q21. A thief is 100 meters ahead of a policeman. Thief runs at 5 km/h, policeman at 10 km/h. How far does the thief run before being caught?

Hint: Relative speed = 10 − 5 = 5 km/h. Find time to close the 100 m gap, then multiply by thief's speed.

✅ 100 meters

Q22. A walks 1 round/hr, B runs 6 rounds/hr, same direction. Starting at 7:30 AM. When do they first cross?

Hint: Same direction → relative speed = 6 − 1 = 5 rounds/hr. Time for B to gain 1 full round on A = 1/5 hr = 12 minutes.

✅ 7:42 AM

Common Mistakes to Avoid

The most frequent errors in this topic aren't conceptual — they're mechanical. Forgetting to convert km/h to m/s before calculating is probably the single biggest source of wrong answers. Always check your units before plugging in numbers.

For relative speed questions, direction matters a lot. Same direction means subtract; opposite direction means add. It's easy to mix these up under exam pressure, so make it a habit to write "same → subtract, opposite → add" at the top of your rough work.

Average speed is another trap. Never average two speeds directly unless the time spent at each is equal. Always go back to total distance ÷ total time.

Wrap Up

Distance-time-speed problems follow very predictable patterns once you've seen enough of them. Train problems almost always use relative speed. Boat-stream problems always use the downstream/upstream split. Ratio-based problems like the walking-slower-reaching-late type follow the inverse relationship between speed and time.

Practice until the setup feels automatic — that's when you stop making careless errors under time pressure.

For more reasoning practice, check out these also

Logrithm

For a structured placement prep roadmap explore,