SSC CGL Maths · Time, Speed and Distance

Speed, Time and Distance Basics

Distance equals speed times time, as long as all three use matching units, and when one of the three is held fixed the other two move in a simple proportion.

All Time, Speed and Distance notes

Why this matters

Seventeen questions in the bank, all EASY, and twelve of them come from the 2025 shifts: a street crossed in a few minutes, a train's speed asked in metres per second, a car whose speed is a ratio of a bus's. They are quick marks when the units are right, and the units are exactly where the wrong options are set.

Concept 1 of 3: Distance equals speed times time

Speed is the ground covered in one unit of time. Cover 40 km in each hour for 3 hours and you have covered 120 km. Every question in this chapter starts from that one line, read forwards or backwards.

Definition

Distance = speed × time, so speed = distance ÷ time and time = distance ÷ speed.
The three must use matching units: km with hours and km/h, metres with seconds and m/s.
Minutes to hours: divide by 60. 45 minutes is 0.75 hour, 48 minutes is 0.8 hour, 20 minutes is $\frac{1}{3}$ hour.
Clock times: first count the hours and minutes between them. From 10:30 a.m. to 2:15 p.m. is 1 h 30 min to noon plus 2 h 15 min, so 3 h 45 min.
Fast route: a rate given per minute times the number of minutes needs no hour conversion at all. It is safe only when the rate and the time use the same unit of time.

Speed, distance and time

d = s \times t \qquad s = \frac{d}{t} \qquad t = \frac{d}{s}

$d$ distance covered
$s$ speed, kept constant
$t$ time taken

Worked example

A bus leaves at 7:40 a.m. and arrives at 11:10 a.m. the same morning, running at 48 km/h. How far does it travel?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 23 Sep 2025, Shift 3 · Q53Easy

Example 1 · Time, Speed and Distance · Speed, Time and Distance Basics

A train starts from a place Mumbai at 6 a.m. and arrives at Kolhapur at 2.30 p.m. on the same day. If the speed of the train is 60 km per hour, find the distance traveled by the train.

Reading 2 hours 30 minutes as 2.3 hours

30 minutes is half an hour, so 2 hours 30 minutes is 2.5 hours. Change minutes to hours by dividing by 60, never by writing them after the decimal point.

Counting clock time across noon

From 9:30 a.m. to 1:00 p.m. is 3 hours 30 minutes. Count up to 12 noon first, then add the afternoon part, instead of subtracting 9 from 1.

Drill 5 more on distance equals speed times time

Concept 2 of 3: Changing km/h to m/s and back

1 km/h means 1000 metres in 3600 seconds, which is

\frac{1000}{3600} = \frac{5}{18}

of a metre every second. So a speed in km/h times

\frac{5}{18}

gives m/s, and a speed in m/s times

\frac{18}{5}

gives km/h.

Definition

km/h to m/s: multiply by $\frac{5}{18}$ . m/s to km/h: multiply by $\frac{18}{5}$ .
Multiples of 18 km/h give whole m/s: 18 is 5, 36 is 10, 54 is 15, 72 is 20, 90 is 25, 108 is 30. Knowing these saves a step in most train and track questions.
Metres per minute to km/h: multiply by 60 and divide by 1000, which is the same as multiplying by 0.06. 100 m a minute is 6 km/h.
The same speed is a smaller number in m/s than in km/h. Use that to check the direction of your fraction.
Fast route: change the given data into the unit the answer asks for at the start, then work in that one unit to the end.

Changing units of speed

1 \text{ km/h} = \frac{5}{18} \text{ m/s} \qquad 1 \text{ m/s} = \frac{18}{5} \text{ km/h}

Worked example

A cyclist crosses a 450 m bridge in 1 minute 15 seconds. What is his speed in km/h?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 21 Sep 2025, Shift 2 · Q54Easy

Example 2 · Time, Speed and Distance · Speed, Time and Distance Basics

An athlete runs a 300-meter race in 24 seconds. How much is his speed in km/h?

Turning the fraction upside down

If changing a speed from km/h to m/s gives a bigger number, the fraction is upside down. 72 km/h is 20 m/s, a smaller number, because a metre is much shorter than a kilometre.

Mixing seconds and minutes with m/s

A speed in m/s needs the time in seconds. 3 minutes at 4 m/s is 180 seconds, so 720 m, not 12 m.

Drill 6 more on changing km/h to m/s and back

Concept 3 of 3: Speed ratios when the time or the distance is fixed

If two people move for the same time, the faster one covers more ground in exactly the ratio of their speeds. If they cover the same ground, the faster one needs less time, in that ratio turned upside down.

Definition

Same time: distance is proportional to speed. Twice the speed, twice the distance.
Same distance: time is inversely proportional to speed. Speeds in the ratio 3 : 4 give times 4 : 3.
Neither fixed: write each speed as distance over time and divide, as in the formula.
"k times as fast" means the speed ratio is k : 1.
Fast route: with ratios you never need the actual distance or time; keep them as letters and they cancel.

Ratio of two speeds

\frac{s_1}{s_2} = \frac{d_1}{d_2} \times \frac{t_2}{t_1}

$d_1, t_1$ distance and time of the first mover
$d_2, t_2$ distance and time of the second mover

Worked example

A truck covers 150 km in 3 hours. A car is 1.4 times as fast as the truck. How far does the car go in 2 hours 30 minutes?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 16 Sep 2025, Shift 2 · Q63Easy

Example 3 · Time, Speed and Distance · Speed, Time and Distance Basics

The ratio of the speeds of a car and a bus is

3 : 4

. If the bus covers a distance of 320 km in 4 hours, what is the speed of the car in km/h?

Using the speed ratio as the time ratio

For the same distance the times are in the inverse ratio. Speeds 2 : 3 give times 3 : 2, so the faster car takes the smaller share of time.

Multiplying the two ratios instead of dividing

Covering a quarter of the distance in three times the time gives a speed ratio of

\frac{1}{4} \div 3 = \frac{1}{12}

, not

\frac{3}{4}

. Divide the distance ratio by the time ratio.

Drill 3 more on speed ratios when the time or the distance is fixed

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 (3)

Distance equals speed times time
Speed, distance and time
$d = s \times t \qquad s = \frac{d}{t} \qquad t = \frac{d}{s}$
Changing km/h to m/s and back
Changing units of speed
$1 \text{ km/h} = \frac{5}{18} \text{ m/s} \qquad 1 \text{ m/s} = \frac{18}{5} \text{ km/h}$
Speed ratios when the time or the distance is fixed
Ratio of two speeds
$\frac{s_1}{s_2} = \frac{d_1}{d_2} \times \frac{t_2}{t_1}$

Watch out for (6)

Reading 2 hours 30 minutes as 2.3 hours
→ Distance equals speed times time
Counting clock time across noon
→ Distance equals speed times time
Turning the fraction upside down
→ Changing km/h to m/s and back
Mixing seconds and minutes with m/s
→ Changing km/h to m/s and back
Using the speed ratio as the time ratio
→ Speed ratios when the time or the distance is fixed
Multiplying the two ratios instead of dividing
→ Speed ratios when the time or the distance is fixed

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