TRAVEL MATHS D T S SPEED DISTANCE TRAVELLED JOURNEY TIME

Calculating Speed D T S Suppose a bus travels 100miles in 2 hours. This is the same as travelling 50 miles in 1 hour. 50 miles in 1 hour is same as 50mph.

SPEED DISTANCE TIME D T S D T S D T S DISTANCE = TIME SPEED X TIME =

D T S Formula for Speed From the previous page we saw that if you travel 100miles in 2hours then your speed is 50mph. NB: 50 = 100  2 Or Speed = Distance  Time By using this formula we can always work out the speed as long as we know the distance travelled and the time taken.

Choosing Speed Units D T S Speeds can be measured in all sorts of ways. The most popular is probably miles per hour or mph. On the Continent this would probably be kilometres per hour or km/h The units of speed depend on the units of distance and the units of time. Consider the following examples.

Example 1 D T S A top sprinter runs 400metres in 50 seconds. Distance in metres & time in seconds. So speed in metres per second or m/s. Using the formula Speed = distance  time = 400  50 m/s. = 8 m/s.

Example 2 D T S A snail crawls 80cm in 4 minutes. Distance in cm & time in minutes. So speed in cm/min. Speed = dist  time = 80  4 cm/min = 20 cm/min

D T S Changing Units Suppose we are given a distance in miles and a time in minutes but we want the speed in mph. We need to express the time in hours. To change minutes into hours we divide by 60. So 15 mins = 15  60 hrs = 0.25hr. Or 20 mins = 20/60 hr = 1/3 hr.

Example 3 D T S The spaceshuttle can travel 2000miles in 10 mins. 10mins = 10/60hr =1/6hr. Speed = dist  time = 2000  1/6 = 12000mph.

Formula for Distance D T S So Distance Travelled = Speed X Time Suppose you are driving at 40mph. Each hour you would cover 40miles. In 2hrs you would cover 80miles. (40 X 2 = 80) In 5hrs you would cover 200miles. (40 X 5 = 200) In 1/2hr you would cover 20miles. (40 X 1/2= 20) So Distance Travelled = Speed X Time

D T S Example 4 A ship sails at 30km/hr. How far will it travel in one day? NB: 1 day = 24 hours! Dist = speed X time = 30 X 24 = 720km

Example 5 D T S A fighter jet flies at 660mph. How far will it travel in 5 mins? 5 Mins = 1/12 hr Now using dist = speed X time we get dist = 660 X 1/12 = 660  12 = 55miles

Example 6 D T S A cargo ship is travelling at 48km/hr. How far will it cover in 3hrs 35mins? NB: 35mins = 35/60hr = 7/12hr. ie time = 3 7/12hrs Dist = speed X time = 48 X 3 7/12 = 172km

Formula for Time D T S So Journey Time = Distance  Speed Suppose you need to travel 100miles. At 100mph it takes 1hr. At 50mph it takes 2hrs. At 25mph it takes 4 hrs. At 10mph it takes 10hrs. At 200mph it only takes 1/2hr. 100  100 = 1 100 50 = 2 100 25 = 4 100 10 = 10 100 200 = 1/2 So Journey Time = Distance  Speed

Example 7 D T S The distance from Edinburgh to London is 400miles. An Intercity train travels at an average speed of 80mph. How long should the journey take? Time = dist  speed = 400  80 = 40  8 = 5 hrs

Example 8 D T S A fighter jet can fly at 630mph. How long should it take to travel 21 miles? (NB use fraction button !) time = dist  speed = 21/630 = 1/30 hr and 1/30 hr = 1/30 X 60 = 2 mins .

Example 9 D T S Total time needed = 2hrs34mins. Gary has to be at a meeting by 3.30pm. He is 120 miles away and reckons he can only do 50mph. He will need 10 mins to park and get to the office. The time is now 12.55pm. Can he make it? Time = dist  speed = 120  50 = 2.4 hrs (0.4 X 60) = 2hrs24mins Total time needed = 2hrs34mins. Arrival time = 12.55pm + 2hrs34mins = 3.29pm He makes it on time . (JUST !)