Speed, Distance and Time

Use distance = speed × time.

So $10\text{ mph}\times 3\text{ h}=30\text{ miles}$.

The cyclist travels 30 miles.

Use speed = distance ÷ time.

So $200\text{ km}÷2\text{ h}=100\text{ km/h}$.

The average speed is 100 km per hour.

Use time = distance ÷ speed.

So $90\text{ km}÷60\text{ km/h}=1.5\text{ h}$.

Since 0.5 of an hour is 30 minutes, this is 1 hour 30 minutes.

(A common slip is to read 1.5 hours as 1 hour 50 minutes, but half an hour is 30 minutes, not 50.)

First convert the time. 1 hour and 30 minutes is 1.5 hours.

Use distance = speed × time. So $12\text{ mph}\times 1.5\text{ h}=18\text{ miles}$.

The cyclist travels 18 miles.

First convert the time. 40 minutes is $40÷60=\frac{2}{3}$ of an hour.

Use speed = distance ÷ time. So $10\text{ km}÷\frac{2}{3}\text{ h}=15\text{ km/h}$.

The average speed is 15 km per hour.

(A common mistake is to write 40 minutes as 0.4 hours, but $10÷0.4=25$, which is wrong.)

Average speed uses the totals, not each part separately.

Total distance is $100\text{ miles}+120\text{ miles}=220\text{ miles}$ and total time is $2\text{ h}+3\text{ h}=5\text{ h}$.

Use speed = distance ÷ time. So $220\text{ miles}÷5\text{ h}=44\text{ mph}$.

The average speed is 44 miles per hour.

(A common mistake is to average the two speeds, 50 and 40, to get 45, but that ignores the different times spent at each speed.)