Unit conversion reflex
Speeds in km/h, lengths in meters: convert first. km/h x 5/18 = m/s.
72 km/h = 72 x 5/18 = 20 m/s.
Trap: Answering in the wrong unit is the most common lost mark in train questions.
Rapid Revision · Quantitative Aptitude
Time, Speed & Distance
Trains, boats and races are one identity, distance = speed x time, plus relative speed. Get the unit conversion reflex right and the rest is bookkeeping.
The 3-minute recap
If you read nothing else tonight, read these 6 lines.
- km/h to m/s: multiply by 5/18. m/s to km/h: multiply by 18/5.
- Same distance at x then y: average speed = 2xy/(x+y).
- Opposite directions: speeds ADD. Same direction: speeds SUBTRACT.
- Train crossing a pole: time = train length / speed. Platform: (train + platform)/speed.
- Boats: downstream = b + s, upstream = b - s; b = (d+u)/2, s = (d-u)/2.
- Same distance, speed ratio a:b means time ratio b:a.
Formula sheet
Every formula for time, speed & distance in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
Core relation
speed = distance / time
Keep units consistent before you plug in.
Unit switch
km/h -> m/s : x 5/18 m/s -> km/h : x 18/5
Relative speed
same direction: |a - b| opposite: a + b
Train past a pole / platform
pole: t = L / speed platform: t = (L + P) / speed
Two trains crossing
t = (L1 + L2) / relative speed
Boats & streams
downstream = b + s upstream = b - s
b = boat speed in still water, s = stream speed.
Average speed
round trip = 2xy / (x + y)
Work through the cards
8 cards, each one idea: what it is, a worked example, and the trap to dodge.
Train past a pole vs a platform
A pole (or a man) has no length: time = L_train / speed. A platform or bridge adds its length: time = (L_train + L_platform) / speed.
200 m train at 20 m/s crosses a 300 m platform in (200+300)/20 = 25 s.
Trap: Forgetting to add the train's OWN length to the platform length.
Relative speed
Two movers: opposite directions add speeds, same direction subtract. Two trains crossing each other cover the SUM of their lengths at relative speed.
150 m and 100 m trains at 30 and 20 m/s head-on: 250 / 50 = 5 s.
Boats and streams
Downstream speed d = boat + stream, upstream u = boat - stream. Recover boat = (d+u)/2 and stream = (d-u)/2.
d = 12, u = 8: boat 10 km/h, stream 2 km/h.
Speed ratio, time ratio
Over the same distance, time is inversely proportional to speed: speed ratio a:b means time ratio b:a.
Speeds 3:4 over one route: times 4:3.
Trap: Inverting the wrong ratio; slower speed always means larger time.
Late-early problems
Same start, same distance, two speeds, one late by t1 and one early by t2: distance = (s1 x s2 / (s2 - s1)) x (t1 + t2), with times in hours.
4 km/h is 10 min late, 5 km/h is 5 min early: d = (20/1) x (15/60) = 5 km.
Average speed is not the midpoint
Average speed = total distance / total time. Only equal TIMES let you average the speeds directly.
Half distance at 30, half at 60: 2 x 30 x 60 / 90 = 40 km/h.
Trap: 45 is the bait; harmonic mean 40 is the answer.
Races
'A beats B by 20 m in 100 m' means when A runs 100, B runs 80: speeds are 100:80 = 5:4. Convert beats-by statements into distance ratios.
A beats B by 10 m and B beats C by 10 m in 100 m: A beats C by 19 m (0.9 x 0.9 = 0.81).
Go deeper
A recap is not practice. These are the creators we rate for real depth on time, speed & distance; full credit to each.
One topic down. Keep the streak going.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.