Fundamentals of Business Mathematics and Statistics · Time and Distance

Speed, Distance and Time Basics for CMA Foundation

Updated 10 October 2026 · Fact-checked

Speed is the distance covered in one unit of time: speed = distance ÷ time. Rearrange it to find distance or time. Convert km/hr to m/sec by multiplying by 5/18. For a journey with unequal distances, average speed is total distance ÷ total time, not the simple average of speeds.

Understand Speed, Distance and Time Basics

Speed tells you how fast something moves. If a car covers 60 km in 1 hour, its speed is 60 km/hr. Three quantities are linked: speed, distance and time. Know any two and you can find the third.

The core relation is speed = distance ÷ time. Rearranged, distance = speed × time, and time = distance ÷ speed. Keep the units consistent. If speed is in km/hr, distance must be in km and time in hours.

Units cause most trouble. To go from km/hr to m/sec, multiply by 5/18 (because 1 km = 1000 m and 1 hr = 3600 sec, and 1000/3600 = 5/18). To go from m/sec to km/hr, multiply by 18/5.

When speed is constant, distance is directly proportional to time. When distance is fixed, speed and time are inversely proportional: if speed rises by a factor, time falls by the same factor.

Average speed is total distance ÷ total time. It is not the plain average of the speeds, unless the time spent at each speed is equal. If you cover the same distance at two speeds x and y, the average speed is 2xy ÷ (x + y), which is the harmonic mean of x and y.

Speed and velocity differ. Speed is only a magnitude. Velocity also has a direction. In CMA Foundation questions you will mostly deal with speed along a straight path.

Key formulas to remember

Basic relation: Speed = Distance ÷ Time; Use consistent units. Distance = Speed × Time and Time = Distance ÷ Speed follow from it.
km/hr to m/sec: x km/hr = x × 5/18 m/sec; Use when distance is in metres or time is in seconds.
m/sec to km/hr: y m/sec = y × 18/5 km/hr; Reverse of the above.
Average speed (general): Average speed = Total distance ÷ Total time; Works for every case.
Average speed, equal distances: Average speed = 2xy ÷ (x + y); Only for two equal distances at speeds x and y.
Same distance, different speeds: Time ratio = inverse of speed ratio; If speeds are in ratio a : b, times are in ratio b : a.
Average speed, equal times: Average speed = (x + y) ÷ 2; Only when equal time is spent at speeds x and y.

How to solve Speed, Distance and Time Basics questions

Use this method for any speed, distance and time question.

1Note what is given and what is asked: speed, distance or time.
2Check the units of every quantity. Convert so they match, using 5/18 or 18/5 when needed.
3Write the relation that links the quantities: S = D ÷ T, D = S × T or T = D ÷ S.
4For a multi-part journey, find the distance and time of each part separately.
5Add the distances and add the times. Use total distance ÷ total time for average speed.
6Substitute and calculate carefully.
7Put the answer in the unit the question asks for.
8Check that the answer is sensible: average speed must lie between the lowest and highest speeds.

Quickest way: Shortcut using ratios and the 5/18 factor

When to use it: Use when the question asks for a conversion, equal-distance average speed, or a change in time due to a change in speed.

For conversions, multiply by 5/18 for m/sec and 18/5 for km/hr.
For equal distances at x and y, use 2xy ÷ (x + y) directly. Do not compute the distance.
If speed changes in ratio a : b over the same distance, time changes in ratio b : a.
For speed increased by a fraction, new time = old time × old speed ÷ new speed.
Eliminate options that are outside the range of the two speeds, or equal to their simple average when distances are equal.

Common mistakes in Speed, Distance and Time Basics

Taking the simple average of two speeds as the average speed when distances are equal
The word 'average' makes students add and halve.
Fix: Use total distance ÷ total time, or 2xy ÷ (x + y). For equal distances, the result is less than the simple average when the speeds differ.
Multiplying by 18/5 when converting km/hr to m/sec
Students mix up the two factors.
Fix: Remember that m/sec numbers are smaller. So km/hr to m/sec uses 5/18, which reduces the number.
Mixing minutes and hours
Times like 30 minutes are used directly with km/hr.
Fix: Convert minutes to hours first: 30 minutes = 1/2 hour, 45 minutes = 3/4 hour.
Using 2xy ÷ (x + y) when the distances are unequal
The formula is memorised without its condition.
Fix: Apply it only if both parts cover the same distance. Otherwise find total distance and total time.
Forgetting that time is inverse to speed
Students scale time up when speed goes up.
Fix: For a fixed distance, higher speed means less time. Write T ∝ 1/S before solving.
Giving the answer in the wrong unit
Students stop once a number is found.
Fix: Reread the question's last line and convert to km/hr, m/sec, minutes or hours as asked.

Worked examples

Example 1

A car travels from Pune to Satara, 60 km, at 40 km/hr and returns at 60 km/hr. Find the average speed for the whole trip.

Show the solution

Time going = 60 ÷ 40 = 1.5 hours.
Time returning = 60 ÷ 60 = 1 hour.
Total distance = 60 + 60 = 120 km.
Total time = 1.5 + 1 = 2.5 hours.
Average speed = 120 ÷ 2.5 = 48 km/hr.
Check with 2xy ÷ (x + y) = 2 × 40 × 60 ÷ 100 = 48 km/hr.

Answer: 48 km/hr

Example 2

A runner covers 400 metres in 50 seconds. Find her speed in km/hr. Then find the time she needs to cover 3.6 km at the same speed.

Show the solution

Speed = 400 ÷ 50 = 8 m/sec.
Convert to km/hr: 8 × 18/5 = 28.8 km/hr.
Time for 3.6 km = 3.6 ÷ 28.8 hours = 0.125 hours.
Convert to minutes: 0.125 × 60 = 7.5 minutes.
Check in metres: 3600 ÷ 8 = 450 seconds = 7.5 minutes.

Answer: Speed = 28.8 km/hr; time = 7.5 minutes

Exam tips

Most questions are one or two steps. Spot whether the question is a conversion, a direct S-D-T find, or an average speed question.
If distances are equal and the options include the simple average, that option is usually a trap.
Convert units before doing anything else. Many wrong options come from unconverted units.
Use ratio thinking for 'speed increases by' or 'time reduces by' questions. It saves calculation time.
Since there is no negative marking, attempt every question. Eliminate options outside the speed range and guess from the rest.

Practice questions from Time and Distance

Speed, Distance and Time Basics: frequently asked questions

What is the speed distance time formula?

Speed = Distance ÷ Time. From it, Distance = Speed × Time and Time = Distance ÷ Speed. Keep units consistent while using them.

How do I convert km/hr to m/s?

Multiply the speed in km/hr by 5/18. For example, 72 km/hr = 72 × 5/18 = 20 m/sec. To go back, multiply m/sec by 18/5.

What is the average speed formula when distance is the same?

If two equal distances are covered at speeds x and y, average speed = 2xy ÷ (x + y). It comes from total distance ÷ total time. It is not valid when the distances are unequal.

What is the difference between speed and velocity?

Speed is how fast an object moves and has only magnitude. Velocity is speed in a stated direction. Foundation questions mostly use speed along a straight path.