SSC CGL Maths · Time, Speed and Distance

Average Speed

Average speed is the whole distance divided by the whole time, which is not the plain average of the speeds unless each speed was kept for the same time.

All Time, Speed and Distance notes

Why this matters

Seventeen questions in the bank, eleven EASY and six MODERATE, seven of them from the 2025 shifts. Most are a journey in parts at different speeds; the rest have equal distances, where a one-line formula replaces the table of times.

Concept 1 of 2: Average speed of a journey in parts

A car that drives 1 hour at 40 km/h and then 1 hour at 80 km/h covers 120 km in 2 hours, so its average is 60 km/h. A car that drives 40 km at 40 km/h and then 40 km at 80 km/h spends longer on the slow part, 1 hour against half an hour, so its average is lower: 80 km in 1.5 hours is about 53.3 km/h. The time spent at each speed decides the average.

Definition

Average speed = total distance ÷ total time. Find each part's time, or each part's distance, then add.
If the parts are given as times, the average is the time-weighted mean of the speeds. Equal times give the plain mean.
If the parts are given as fractions of the journey, pick a total distance that every speed divides into, then add the times. The answer does not depend on the distance you pick.
Unknown part: write total distance = average speed × total time as an equation and solve for the missing time or speed.
A rest or a halt counts in the total time but adds no distance.

Average speed

\bar{s} = \frac{d_1 + d_2 + d_3}{t_1 + t_2 + t_3} \qquad \bar{s} = \frac{s_1t_1 + s_2t_2}{t_1 + t_2}

$\bar{s}$ average speed for the whole journey
$d_1, t_1$ distance and time of the first part
$s_1$ speed during the first part

Worked example

A van covers 90 km at 45 km/h and then 150 km at 60 km/h. What is its average speed for the whole trip?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 24 Sep 2025, Shift 1 · Q53Moderate

Example 1 · Time, Speed and Distance · Average Speed

Jayesh covers one-fourth of his journey at 20 km/h, another one-fourth at 10 km/h, and the rest at 70 km/h. What is his average speed?

Averaging the speeds

The mean of 40 and 80 is 60, but the average speed is 60 km/h only if equal TIMES were spent at each speed. For equal distances it is lower, because more time goes on the slower part.

Leaving a halt out of the time

A stop adds time and no distance, so it lowers the average speed. Include it in the total time unless the question asks for the speed while moving.

Drill 8 more on average speed of a journey in parts

Concept 2 of 2: Average speed over equal distances

When each speed is kept for the same distance, the total distance and the total time can be written with the speeds alone, and the distance cancels. That is why these questions can be answered without ever knowing the distance.

Definition

Two equal distances at speeds $a$ and $b$ : average $= \frac{2ab}{a + b}$ . A round trip, out at one speed and back at another, is this case.
Three equal distances at $a$ , $b$ and $c$ : average $= \frac{3abc}{ab + bc + ca}$ .
The answer always lies below the plain mean of the speeds, nearer the slower one.
Round trip with the total time given: the one-way distance is the total time divided by $\frac{1}{a} + \frac{1}{b}$ .
Fast route: take each distance as the LCM of the speeds, so every time is a whole number, and divide the total distance by the total time.
Limit: both formulas need equal distances. Unequal distances go back to total distance over total time.

Average speed over equal distances

\bar{s} = \frac{2ab}{a + b} \qquad \bar{s} = \frac{3abc}{ab + bc + ca}

$a, b, c$ the speeds, each kept for the same distance

Worked example

A courier rides to a depot at 36 km/h and returns along the same road at 54 km/h. What is his average speed for the round trip?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 26 Sep 2025, Shift 3 · Q59Easy

Example 2 · Time, Speed and Distance · Average Speed

A car covers three equal distances at speeds of 30 km/h, 45 km/h, and 90 km/h, respectively. What is the average speed of the car for the entire journey?

Using 2ab/(a + b) when the times are equal

The formula is for equal distances. When equal times are spent at each speed, the average speed is the plain mean (a + b) ÷ 2.

Taking the average speed as the one-way distance

With a total time given, 2ab/(a + b) gives a speed. The whole round trip is that speed times the total time, and the one-way distance is half of it.

Drill 7 more on average speed over equal distances

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Average speed of a journey in parts
Average speed
$\bar{s} = \frac{d_1 + d_2 + d_3}{t_1 + t_2 + t_3} \qquad \bar{s} = \frac{s_1t_1 + s_2t_2}{t_1 + t_2}$
Average speed over equal distances
Average speed over equal distances
$\bar{s} = \frac{2ab}{a + b} \qquad \bar{s} = \frac{3abc}{ab + bc + ca}$

Watch out for (4)

Averaging the speeds
→ Average speed of a journey in parts
Leaving a halt out of the time
→ Average speed of a journey in parts
Using 2ab/(a + b) when the times are equal
→ Average speed over equal distances
Taking the average speed as the one-way distance
→ Average speed over equal distances

Test yourself on Time, Speed and Distance

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Time, Speed and Distance chapter test Drill all 17 questions