148. Speed, Distance and Time

Learning Intentions

• To understand that speed is a rate relating distance and time
• Solve an average speed (given a distance and the time taken)
• find the distance travelled (given an average speed and the time taken)
• find the time taken (given an average speed and the distance)
• convert between different units of speed

Pre-requisite Summary

• Know that a rate compares two quantities measured in different units
• Understand that distance is measured in units such as m and km, and time in units such as s, min and h
• Be able to convert between units of time
• Be able to convert between units of length
• Be able to multiply and divide whole numbers and decimals accurately
• Understand that average means total amount divided by total number of equal units
• Know that “per” means “for each” or “for one”

Worked Examples

Worked Example 1

State what each speed means:

a)

b)

c)

Worked Example 2

Find the average speed:

a) km travelled in h

b) m travelled in s

c) km travelled in h

Worked Example 3

Find the distance travelled:

a) speed , time h

b) speed , time s

c) speed , time h

Worked Example 4

Find the time taken:

a) distance km, speed

b) distance m, speed

c) distance km, speed

Worked Example 5

Convert between units of speed:

a) to

b) to

c) to

Worked Example 6

Solve each worded problem:

a) A car travels km in h. Find its average speed.

b) A cyclist rides at for h. Find the distance travelled.

c) A runner travels m at an average speed of . Find the time taken.

Problems

Problem 1

State what each speed means:

a)

b)

c)

Problem 2

Find the average speed:

a) km travelled in h

b) m travelled in s

c) km travelled in h

Problem 3

Find the distance travelled:

a) speed , time h

b) speed , time s

c) speed , time h

Problem 4

Find the time taken:

a) distance km, speed

b) distance m, speed

c) distance km, speed

Problem 5

Convert between units of speed:

a) to

b) to

c) to

Problem 6

Solve each worded problem:

a) A bus travels km in h. Find its average speed.

b) A swimmer moves at for s. Find the distance travelled.

c) A train travels km at an average speed of . Find the time taken.

Exercises

Understanding and Fluency

Exercise 1.

Complete each statement:

a) Speed is a ______ relating distance and time

b) Average speed is found by dividing ______ by ______

c) Distance is found by multiplying ______ by ______

d) Time is found by dividing ______ by ______

Exercise 2.

State what each speed means:

a)

b)

c)

d)

Exercise 3.

Find the average speed:

a) km in h

b) km in h

c) m in s

Exercise 4.

Find the average speed:

a) m in s

b) km in h

c) km in h

Exercise 5.

Find the distance travelled:

a) for h

b) for s

c) for h

Exercise 6.

Find the time taken:

a) km at

b) m at

c) km at

Exercise 7.

Convert between units of speed:

a) to

b) to

c) to

d) to

Exercise 8.

Solve each:

a) A car travels at for h. Find the distance.

b) A bike travels km in h. Find the average speed.

c) A runner travels m at . Find the time taken.

Reasoning

Exercise 9.

Explain why speed is a rate and not just a single measurement.

Exercise 10.

A student says that average speed is found by adding the distance and the time. Explain the mistake.

Exercise 11.

Noah says that if a car travels at for h, then the distance is km. Is he correct? Explain.

Exercise 12.

Explain why the units are important when writing an answer for speed.

Exercise 13.

A student says that . Describe the error.

Problem-solving

Exercise 14.

A train travels km in h. Find its average speed.

Exercise 15.

A boat moves at for h. Find the distance travelled.

Exercise 16.

A runner travels m at an average speed of . Find the time taken.

Exercise 17.

A car travels at . Convert this speed to .

Exercise 18.

A cyclist travels km in h. Find the average speed.

Exercise 19.

A bus travels at for h. Find the distance travelled.

Potential Misunderstandings

• Students may confuse speed with distance or time
• Students may Use the wrong formula, such as dividing time by distance
• Students may add distance and time instead of dividing or multiplying
• Students may forget to include units such as km/h or m/s in the answer
• Students may mix kilometres with seconds or metres with hours without converting
• Students may think average speed means the speed at one instant rather than over the whole trip
• Students may make errors converting between km/h and m/s
• Students may divide when they should multiply when finding distance
• Students may multiply when they should divide when finding time

Next: 149e. Unitary Method for Ratios and Rates