# TRAVEL MATHS D S n SPEED n DISTANCE

• Slides: 17

TRAVEL MATHS D S n SPEED n DISTANCE TRAVELLED n JOURNEY TIME T

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

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

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

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

D Example 1 n n n n S A top sprinter runs 400 metres 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. T

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

D Changing Units S n Suppose we are given a distance in miles and a time in minutes but we want the speed in mph. n We need to express the time in hours. n To change minutes into hours we divide by 60. n So 15 mins = 15 60 hrs = 0. 25 hr. n Or 20 mins = 20/60 hr = 1/3 hr. T

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

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

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

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

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

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

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

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

Example 9 D S n n n T Gary has to be at a meeting by 3. 30 pm. He is 120 miles away and reckons he can only do 50 mph. He will need 10 mins to park and get to the office. The time is now 12. 55 pm. Can he make it? Time = dist speed = 120 50 = 2. 4 hrs (0. 4 X 60) = 2 hrs 24 mins Total time needed = 2 hrs 34 mins. Arrival time = 12. 55 pm + 2 hrs 34 mins = 3. 29 pm He makes it on time. (JUST !)