In a speed problem, the first step is to write the minutes as a fraction of an hour. Once the time is in hours, you multiply to find the distance, as in 90 × 1/3 = 30 km in 20 minutes, and you divide to find the time or the speed. The same steps work in miles and mph: 60 mph for 20 minutes is 60 × 1/3 = 20 miles.
| To find | Formula | With 72 km/h and 5/6 h |
|---|---|---|
| Distance | d = v × t | 72 × 5/6 = 60 km |
| Speed | v = d ÷ t | 60 ÷ 5/6 = 72 km/h |
| Time | t = d ÷ v | 60 ÷ 72 = 5/6 h |
The three formulas are one relationship written three ways, and in all three the time is in hours when the speed is in km/h. That is why the first step in almost every problem is converting the minutes.
Turning minutes into a fraction of an hour
An hour has 60 minutes, so each minute is 1/60 of an hour. Write the minutes over 60 and simplify by dividing by the GCF (greatest common factor) of the two numbers. If the time mixes hours and minutes, keep the whole hours and convert only the rest. The table gathers the conversions that come up most often in word problems.
| Minutes | Fraction of an hour | As a mixed number of hours |
|---|---|---|
| 30 | 1/2 | 1 h 30 min = 3/2 h |
| 45 | 3/4 | 1 h 45 min = 7/4 h |
| 20 | 1/3 | 2 h 20 min = 7/3 h |
| 40 | 2/3 | 1 h 40 min = 5/3 h |
| 12 | 1/5 | 1 h 12 min = 6/5 h |
Check each row by multiplying the fraction by 60. The fraction of an hour to minutes converter covers any other fraction and is handy for checking a result before you turn it in.
The same care applies to decimals. 1.30 h is 1.30 × 60 = 78 min, which is 1 h 18 min, not 1 h 30 min. Round only at the end: writing 2/3 h as 0.67 h changes the result, while the fraction keeps it exact. To multiply and divide fractions step by step, you can use the multiplying fractions calculator and the dividing fractions one.
Worked example: how long a car takes to cover 50 km at 40 km/h
A car travels at 40 km/h and has to cover 50 km. How long does it take, in hours and in minutes?
- Choose the time formula. The time is missing, so t = d ÷ v.
- Divide. t = 50 ÷ 40 = 5/4 h.
- Split off the whole hour. 5/4 = 1 + 1/4, which is 1 1/4 h.
- Turn the fractional part into minutes. 1/4 × 60 = 15 min.
Answer: 5/4 h, which is 1 h 15 min.
Check: 40 × 5/4 = 50 km, the distance in the problem. Also, 40 km/h covers 40 km in one hour, so 50 km has to take a bit more than an hour.
Two vehicles approaching or chasing each other
When two vehicles are involved, you work out the speed at which the distance between them shrinks. If they head toward each other, you add the speeds. If they go in the same direction, you subtract them, because only what the faster one gains on the slower one counts. Then you divide the distance between them by that closing speed.
For a meeting, picture two cars 225 km apart that leave at the same time, heading toward each other at 80 and 70 km/h. The gap shrinks by 80 + 70 = 150 km every hour, so they pass each other after 225 ÷ 150 = 3/2 h, which is 90 minutes. The first has covered 80 × 3/2 = 120 km and the second 70 × 3/2 = 105 km, which add up to the 225 km.
Worked example: a cyclist catching up with a walker
A walker sets out at 5 km/h. Twenty minutes later a cyclist sets out at 15 km/h along the same path. How long does the cyclist take to catch the walker, and how far from the start is that?
- Find the head start. 20 min = 1/3 h, so the walker is 5 × 1/3 = 5/3 km ahead.
- Find the closing speed. 15 − 5 = 10 km/h.
- Divide the head start by the closing speed. (5/3) ÷ 10 = 1/6 h, which is 10 min.
- Find the meeting point. The cyclist covers 15 × 1/6 = 5/2 km.
Answer: the cyclist catches the walker after 10 min, 2.5 km from the start.
Check: the walker has walked 20 + 10 = 30 min, or 1/2 h, and 5 × 1/2 = 5/2 km. Both are at the same spot.
The head start is the distance the first traveler has covered when the second one sets out, so it is found with the difference in departure times, not with the time until they meet. The work rate problems guide uses the same reasoning with rates that combine, using flow rates instead of kilometers.
From m/s to km/h, and average speed
To convert m/s to km/h, multiply by 18/5, which is 3.6. So 15 m/s × 18/5 = 54 km/h. To go the other way, multiply by 5/18. If the speeds differ on a round trip, the average speed is not the average of the two: it is the total distance divided by the total time. With 40 km at 20 km/h (2 h) and 40 km at 40 km/h (1 h), the 80 km trip takes 3 h and the average is 80 ÷ 3 = 80/3 km/h, which is ≈ 26.7 km/h (error under 0.04 km/h), not the 30 you get from a simple average. The article on average speed on a round trip explains why the harmonic mean comes out and shows a table with more pairs of speeds.
When a problem gives two quantities and asks for a third, you can also set it up as a direct proportion. The rule of three solves, for example, how many kilometers you cover in a different time at the same speed, and the guide to ratio, proportion and fraction explains why it works. All of this assumes constant speed. If the vehicle speeds up or slows down, the result is an estimate.
Practice
- A train goes at 60 km/h for 1 1/4 h. How far does it travel?
- A cyclist covers 24 km in 40 minutes. How fast is the cyclist going?
- Two cyclists set out from two towns 36 km apart and ride toward each other at 10 and 8 km/h. How long until they meet?
Show the answers
- 75 km, because 1 1/4 h is 1.25 h and 60 × 1.25 = 75.
- 36 km/h, because 40 min = 2/3 h and 24 ÷ 2/3 = 36.
- 2 h, because 10 + 8 = 18 km/h and 36 ÷ 18 = 2.
For more multiplying and dividing practice, the fraction worksheet generator creates printable sheets. If you want to check a result with another method, the guide to verifying a fraction answer gathers several checks, and the applications hub groups the guides that use fractions in everyday situations.
Sources
Wikipedia, article Speed, section “Average speed”: defines average speed as the total distance covered divided by the time interval, which is the quantity used for the round-trip average (accessed October 17, 2026).