Speed, Distance & Time · Topic 4 of 5

🔀 Relative Speed

3 exam question types, fully solved

When two bodies move, what matters is how fast the gap between them changes — the relative speed. One rule decides everything: add the speeds when they move opposite ways, subtract when they move the same way.

Add for opposite, subtract for same direction

• Opposite directions / toward each other: the gap shrinks at the SUM, . Meeting time .

• Same direction / chase / overtake: the gap closes at the DIFFERENCE, . Catch-up time . A head start in time becomes a distance lead first: .

• After-crossing trick: two bodies start together from opposite ends; if after meeting they take and more time to finish, their speed ratio is (square root of the SWAPPED times). The one that finishes faster is the quicker body.

🚗Journey SimulatorWatch the gap close at relative speed

🚗 A speed: 60 km/h

🚙 B speed: 40 km/h

↔ Start gap: 200 km

⏱ drag time

Every hour the gap shrinks by 60 + 40 = 100 km, so a 200 km gap is gone in 2 h.

Relative Speed

100 km/h

60 + 40

Time to Meet

2 h

200 ÷ 100

A travels

120 km

60 × 2.00

Two bodies 120 km apart move toward each other at 45 and 75 km/h; relative speed km/h.

Q1Two trains are 120 km apart and move toward each other at 45 km/h and 75 km/h. They meet after:

Q2A thief is 1 km ahead of a policeman and runs at 10 km/h, while the policeman chases at 12 km/h in the same direction. The thief is caught after:

Q3Two bodies start at the same time from opposite ends and move toward each other. After meeting, A takes 25 hrs and B takes 9 hrs to finish. The ratio of A speed to B speed is:

📚

Real exam questions — Relative Speed

3 question types · 9 solved examples from real SSC papers

Add speeds when bodies move toward each other, subtract when they move the same way, and use the $\sqrt{b}:\sqrt{a}$ trick for after-crossing speed ratios.

How to solve this type

Picture two people walking straight at each other. Each second, the gap between them shrinks by BOTH of their speeds together — so the speed that matters (the "relative speed") is the sum.

The master formula is

\text{time to meet}=\dfrac{\text{distance between them}}{S_1+S_2}

.

Steps: (1) confirm the words say "toward each other" / "opposite ends" / "meet"; (2) add the two speeds; (3) divide the starting gap by that sum. If speeds are in km/h keep distance in km and time in hours; convert km/h to m/s with

\times\dfrac{5}{18}

only when lengths are in metres.

For clock problems, find the gap at the moment BOTH have started moving, then add that travel time to the later start time.

A and B are 400 km apart. A moves at 50 km/h and B at 30 km/h toward each other. After how long do they meet?

A4 hrsB3 hrsC5 hrsD6 hrs

A and B are 300 km apart. A travels at 40 km/h and B at 60 km/h toward each other. They meet after:

A2.5 hrsB3 hrsC4 hrsD5 hrs

P leaves at 8 a.m. at 20 km/h. At 10 a.m. Q is 200 km away and moves toward P at 30 km/h. At what time do they meet?

A2 p.m.B1 p.m.C12 noonD11 a.m.