# Time, Speed and Distance — Formulas, Relative Speed and Tricks

Source: https://skills101.in/learn/aptitude/time-speed-and-distance — Skills101 free tutorial (Quantitative Aptitude). Updated 2026-11-09.

Every question in this chapter comes from one formula.

![The D-S-T triangle: Distance on top, Speed and Time at the bottom. Cover what you want to find. km/h to m/s multiply by 5/18](https://skills101.in/learn-img/aptitude/dst-triangle.svg)

> **Distance = Speed × Time**   →   Speed = D ÷ T,   Time = D ÷ S

## 1. Units

- **km/h → m/s: × 5/18**  (72 km/h = 72 × 5/18 = **20 m/s**)
- **m/s → km/h: × 18/5**  (15 m/s = 15 × 18/5 = **54 km/h**)

Always check that distance, speed and time are in matching units before calculating.

### Example 1
*A bus covers 180 km in 3 hours 45 minutes. Find its speed.*

3 h 45 min = 3.75 h → speed = 180 ÷ 3.75 = **48 km/h**.

## 2. Speed and time are inverses

For the **same distance**, if speed is multiplied by k, time is divided by k.

### Example 2
*Walking at 3/4 of his usual speed, a man is 20 minutes late. What is his usual time?*

New speed = ¾ → new time = 4/3 of usual. The extra ⅓ of the usual time = 20 min → usual time = **60 minutes**.

### Example 3 — late and early
*At 40 km/h a student reaches school 6 minutes late. At 60 km/h, 4 minutes early. Find the distance.*

The time difference is 6 + 4 = 10 minutes = 1/6 hour.

D/40 − D/60 = 1/6 → (3D − 2D)/120 = 1/6 → D = **20 km**.

## 3. Average speed

Total distance ÷ total time. For the **same distance** at speeds a and b:

> **Average speed = 2ab ÷ (a + b)**

### Example 4
*A cyclist rides 12 km at 6 km/h and then 12 km at 12 km/h. Average speed?*

2 × 6 × 12 ÷ 18 = **8 km/h**. (Check: time = 2 + 1 = 3 h for 24 km ✓)

## 4. Relative speed

![Same direction: 60 and 40 km/h close the gap at 20 km/h. Opposite directions: 60 and 40 km/h close the gap at 100 km/h](https://skills101.in/learn-img/aptitude/relative-speed.svg)

- **Same direction → subtract** the speeds
- **Opposite directions → add** the speeds

### Example 5 — meeting
*Two people start 90 km apart and walk towards each other at 5 km/h and 4 km/h. When do they meet?*

Relative speed = 9 km/h → time = 90 ÷ 9 = **10 hours**.

### Example 6 — chasing
*A thief runs at 8 km/h. A policeman starts chasing him 15 minutes later at 10 km/h. How long until he catches him?*

Head start = 8 × ¼ = 2 km. Relative speed = 2 km/h → time = 2 ÷ 2 = **1 hour**.

## 5. Ratio thinking

If two people race for the same time, distances are in the ratio of speeds. If they cover the same distance, times are in the **inverse** ratio of speeds.

### Example 7
*The speeds of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a place. How long does A take?*

Time ratio = 4 : 3. The difference of 1 part = 20 min → A = 4 × 20 = **80 minutes**.

## 6. Races

*"A beats B by 20 m in a 100 m race"* means when A finishes 100 m, B has run 80 m. So their speeds are in the ratio 100 : 80 = 5 : 4.

### Example 8
*In a 1 km race, A beats B by 100 m and B beats C by 100 m. By how much does A beat C?*

When A runs 1000, B runs 900. When B runs 1000, C runs 900 → when B runs 900, C runs 810. So A beats C by 1000 − 810 = **190 m**.

## Common mistakes

- Mixing km/h with metres and seconds. Convert first.
- Averaging speeds as (a + b)/2.
- Adding speeds for people moving in the **same** direction.

## Quick recap

- D = S × T; × 5/18 for km/h → m/s.
- Same distance: time ∝ 1/speed.
- Same distance twice: average speed = 2ab/(a + b).
- Same direction subtract, opposite direction add.


Practice quiz and free certificate: https://skills101.in/learn/aptitude/time-speed-and-distance