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Teach GCSE Maths Speed

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**Speed Teach GCSE Maths © Christine Crisp**

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**Suppose we travel 80 km in 1 hour.**

At times we could be travelling very fast and at others we might have stopped at traffic lights. Sometimes we will be accelerating and sometimes slowing down. However, from the information that we travelled 80 km in 1 hour, we can find the average speed. The average speed is 80 km per hour. If I travel the next 40 km in 1 hour my average speed for this 2nd hour is halved to 40 km per hour. The average speed for the journey is 60 km per hour.

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**We can use a graph to find the average speed.**

40 km/h 40 km 1st hour: 80 km 80 km/h 80 km 2nd hour: 40 km 1 hour 1 hour If we draw a graph of distance and time, the average speed is given by how steep the line is. average speed = distance time

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**d s t distance average speed = time**

We can use this formula to find either: speed if we know distance and time, or distance if we know speed and time, or time if we know distance and speed. Tip: A way to remember this formula: Write d, s, and t in alphabetical order in a “warning” triangle. d s t

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**d d s t t distance average speed = time**

We can use this formula to find either: speed if we know distance and time, or distance if we know speed and time, or time if we know distance and speed. Tip: A way to remember this formula: Write d, s, and t in alphabetical order in a “warning” triangle. d d Tip: Check the letters are in the right order by noting the units for speed. e.g. km/h, kilometres over hours. s t t

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**d s t average speed = distance time**

We can use this formula to find either: speed if we know distance and time, or distance if we know speed and time, or time if we know distance and speed. Tip: A way to remember this formula: Write d, s, and t in alphabetical order in a “warning” triangle. d For distance cover up the d. For time cover up the t. For speed cover up the s. s t The triangle gives d over t (distance over time). speed is distance over time. time is distance over speed. distance is speed time

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e.g.2 Find the time taken, in minutes, to travel 30 miles at an average speed of 40 mph ( miles per hour ). d Solution: s t time = 30 time = distance speed hour 40 = 0·75 hour Since the distance is in miles and the speed in mph, the time is in hours. We will have to change it to minutes. Tell your partner how many minutes are in 0·75 ( or three quarters ) of an hour. Ans: 45 mins If we don’t recognise the answer, to change from hours to minutes we multiply by 60.

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e.g.3 Without using a calculator, find the distance travelled on a trip that takes 20 minutes if the average speed is 6 km/h. Solution: Without a calculator, if we have mixed units . . .

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e.g.3 Without using a calculator, find the distance travelled on a trip that takes 20 minutes if the average speed is 6 km/h. Solution: Without a calculator, if we have mixed units . . . it is often easier not to use the formula. A speed of 6 km/h means 6 km travelled in 1 hour ( or 60 minutes ). This is 1 km in 10 minutes or 2 km in 20 minutes. The answer is 2 km.

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SUMMARY We can use a warning triangle to find the formula that links average speed, distance and time. d s t letters in alphabetical order, average speed = distance time time = distance speed distance = speed time If the units for speed are km/h, the units for distance must be km and for time must be hours. Non-calculator problems are usually easier without the formula.

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EXERCISE 1. Find the average speed if a car travels a distance of 220 km in 4 hours. 2. Find the distance walked in three and a half hours at an average speed of 2 mph. 3. Find the time taken to run 5 km at an average speed of 8 km/h. Give your answer in minutes. 4. Without using a calculator, find the average speed for a journey of 10 miles in 15 minutes. Give your answer in miles per hour.

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**d s t = = 55 km/hour d s t = 2 3·5 = 7 miles EXERCISE**

1. Find the average speed if a car travels a distance of 220 km in 4 hours. Solution: d s t average speed = distance time 220 4 = = 55 km/hour 2. Find the distance walked in three and a half hours at an average speed of 2 mph. Solution: distance = speed time d s t = 2 3·5 = 7 miles

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**d s t = = 0·625 hours = 0·625 60 minutes = 37·5 minutes EXERCISE**

3. Find the time taken to run 5 km at an average speed of 8 km/h. Give your answer in minutes. Solution: time = distance speed d s t 5 8 = = 0·625 hours = 0·625 60 minutes = 37·5 minutes

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**10 miles in 15 minutes 20 miles in 30 minutes 40 miles in 60 minutes**

EXERCISE 4. Without using a calculator, find the average speed for a journey of 10 miles in 15 minutes. Give your answer in miles per hour. Solution: We need to find the distance travelled in 1 hour ( 60 minutes ). We have the distance travelled in 15 minutes. 10 miles in 15 minutes Doubling the numbers: 20 miles in 30 minutes Doubling again: 40 miles in 60 minutes The average speed is 40 mph.

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