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TRAVEL MATHS TRAVEL MATHS SPEED SPEED DISTANCE TRAVELLED DISTANCE TRAVELLED JOURNEY TIME JOURNEY TIME D TS

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

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D TS D TS D TS SPEED DISTANCE =TIME DISTANCE = SPEED XTIME = DISTANCE SPEED

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

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Choosing Speed Units Choosing Speed Units Speeds can be measured in all sorts of ways. The most popular is probably miles per hour or mph. 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 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. The units of speed depend on the units of distance and the units of time. Consider the following examples. Consider the following examples. D TS

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

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

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

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

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

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

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

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

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

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

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

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

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