Relative Speed: Trains, Boats and Streams

Relative speed turns two moving objects into one problem by combining their speeds, and it powers the two most frequent SBI Clerk word-problem families: trains and boats-and-streams. Get the one rule right — add speeds when objects move towards each other or in opposite directions, subtract when they move the same way — and both families collapse into simple distance-over-speed sums. This is high-yield territory, so the small effort here returns marks in almost every prelims paper.

The Relative Speed Rule

When two bodies move in opposite directions, their relative speed is the sum of their speeds, because they close or open the gap faster. When they move in the same direction, the relative speed is the difference, since the faster one only slowly gains on the slower. A question about two trains passing each other, or a faster train overtaking a slower one, is answered by choosing sum or difference and then dividing the combined length by that relative speed. Nothing more complicated than that is ever required.

Opposite directions: relative speed = a + b Same direction: relative speed = a − b

Train Crossing a Pole versus a Platform

A train crossing a stationary pole or a standing man travels a distance equal to just its own length, because the pole has no length. A train crossing a platform or a bridge travels its own length plus the platform's length. This single distinction settles most train sums: identify whether the object crossed has a length of its own. Time equals total distance divided by the train's speed in m/s, so remember to convert the speed with 5/18 before you divide, or your seconds will be wrong.

✗ Using only the train's length when it crosses a 200 m platform  |  ✓ Adding train length + 200 m platform, then dividing by speed

Boats and Streams

In still water a boat has its own speed; a stream adds to it downstream and subtracts from it upstream. So downstream speed = boat + stream, and upstream speed = boat − stream. From any two of these you can recover the others: boat speed is the average of the downstream and upstream speeds, and stream speed is half their difference. These two recovery formulas are the heart of every boats-and-streams question and are worth memorising word for word, because most sums simply ask you to apply them.

Downstream = b + s Upstream = b − s Boat = (D + U)/2 Stream = (D − U)/2

Solved Examples

Example 1: Two trains 120 m and 180 m long run towards each other at 40 and 50 km/hr. Relative speed = 90 km/hr = 25 m/s; time = 300/25 = 12 s. Example 2: A 150 m train at 72 km/hr (20 m/s) crosses a 250 m bridge in (150+250)/20 = 20 s. Example 3: A boat does 18 km/hr downstream and 12 km/hr upstream, so boat = 15 and stream = 3 km/hr.

Choosing Sum or Difference Fast

Under time pressure the only decision that matters is sum versus difference, so train your eye to read direction first. Words like 'towards each other', 'cross each other' or 'opposite directions' mean add; words like 'overtakes', 'in the same direction' or 'faster train catches up' mean subtract. For boats, 'downstream' and 'with the current' mean add, while 'upstream' and 'against the current' mean subtract. Fixing this vocabulary in advance means you never pause mid-question, and the arithmetic that follows is always a one-step division.