Time, Speed and Distance

Planning Trips and Interpreting Travel Data Based on Maps

CAPS Grade 10 Mathematical Literacy

In Grade 10 Mathematical Literacy, the Time-Speed-Distance relationship is used to plan trips or interpret travel data based on maps. It connects the physical distance measured on a map to the practical reality of how long a journey will take.

Time-Speed-Distance Overview

The relationship between time, speed and distance is fundamental to understanding travel and movement in the real world. By combining this relationship with map reading and scale calculations, you can plan journeys, estimate arrival times, and determine if speed limits are being followed.

Key Concepts

Distance Speed Time Average Speed Decimal Time Unit Conversion Speed Limits Arrival Times

The Core Formula

Time-Speed-Distance Triangle

Relationship Formula

Distance = Speed � Time

Speed = Distance � Time

Time = Distance � Speed

The relationship is defined by three variations of the same formula. Which one you use depends on what information you have and what you need to find.

Distance = Speed � Time
Find how far you travelled. Example: 60 km/h � 2 h = 120 km
Speed = Distance � Time
Find how fast you were going. Example: 240 km � 3 h = 80 km/h
Time = Distance � Speed
Find how long the trip took. Example: 180 km � 60 km/h = 3 hours
Memory Aid
Cover the value you want to find in the triangle: D at top, S and T at bottom.

Integration with Maps

1

Measure Map Distance

Find the distance between two points on the map using a ruler.

Measurement Tips: Use a ruler for straight lines. For curved roads, use string or measure in segments. Record measurement in centimeters (cm).
2

Convert Using Map Scale

Convert measurement to actual distance using the map scale.

Scale Conversion: Number scale: multiply by scale denominator. Bar scale: measure bar to find ratio first.
3

Apply Time-Speed-Distance Formula

Apply actual distance to one of the formulas to calculate travel time or required speed.

Example: Distance = 42.5 km, Speed = 85 km/h ? Time = 42.5 � 85 = 0.5 hours = 30 minutes

Handling Time (The "Common Trap")

1

Understanding Decimal Time vs Clock Time

Calculators use decimal time, but time is measured in 60-minute increments.

Key Concept: 1 hour = 60 minutes, 0.5 hours = 30 minutes, 0.25 hours = 15 minutes, 0.1 hours = 6 minutes.
Common Trap: 2.25 hours is NOT 2 hours 25 minutes! It is 2 hours and 15 minutes (0.25 � 60 = 15).
2

Decimal to Minutes Conversion

To convert decimal hours to hours and minutes, multiply the decimal part by 60.

Formula: Minutes = Decimal Part � 60
Examples: 2.4 hours = 2h24m, 3.75 hours = 3h45m, 1.2 hours = 1h12m, 0.8 hours = 48m
3

Minutes to Decimal Conversion

To convert minutes to decimal hours, divide the minutes by 60.

Formula: Decimal Hours = Minutes � 60
Examples: 30m = 0.5h, 45m = 0.75h, 15m = 0.25h, 2h20m = 2.333h

Speed Limits and Reality

Average Speed

Average speed is total distance travelled divided by total time taken, including any stops along the way.

1

Trip covers 240 km. Stop for 30 minutes. Total time = 4 hours. Average speed = 240 � 4 = 60 km/h

Speed Limits

South African speed limits: Urban areas 60-80 km/h, Rural roads 100 km/h, Freeways 120 km/h.

U

Urban Areas: 60 km/h (residential) to 80 km/h (main roads)

R

Rural Roads: 100 km/h

F

Freeways/Highways: 120 km/h

Arrival Times

Calculate when you will arrive based on departure time, distance, and speed.

1

120 km trip at 80 km/h, depart 08:00. Time = 120 � 80 = 1.5 hours = 1h30m. Arrival = 09:30

Unit Consistency

Matching Units

Critical Requirement

km/h ? km ? hours

m/s ? m ? seconds

Always ensure your units match before calculating. Mixing units is one of the most common sources of error.

Speed in km/h
Distance must be in km, Time in hours. Convert meters to km (�1000), minutes to hours (�60).
Speed in m/s
Distance must be in m, Time in seconds. Convert km to m (�1000), hours to seconds (�3600).
Common Conversions
km to m: �1000, m to km: �1000, hours to minutes: �60, minutes to hours: �60
Speed Conversions
km/h to m/s: � 3.6, m/s to km/h: � 3.6 (Example: 72 km/h = 20 m/s)

Worked Examples

Example 1: Finding Time

Map scale 1:500,000, distance 6.5 cm, speed 100 km/h.

Solution

Actual = 6.5 � 500,000 = 32.5 km. Time = 32.5 � 100 = 0.325 h = 19.5 minutes

Example 2: Finding Speed

15 km in 3h20m. Find average speed.

Solution

3h20m = 3.333h. Speed = 15 � 3.333 = 4.5 km/h

Example 3: Arrival Time

Depart 07:45, 180 km at 80 km/h.

Solution

Time = 180 � 80 = 2.25h = 2h15m. Arrival = 10:00

Example 4: Speed Check

45 km in 25 minutes on freeway (120 km/h limit).

Solution

25m = 0.4167h. Speed = 45 � 0.4167 = 108 km/h ? Not speeding

Interactive Time-Speed-Distance Challenge

Question 1: If you travel at 80 km/h for 2.5 hours, how far do you go?
Question 2: How many minutes is 3.75 hours?
Question 3: A trip of 150 km takes 2 hours. What is the average speed?
Question 4: You leave at 09:30 and travel for 2 hours 45 minutes. When do you arrive?
Question 5: A driver covers 60 km in 45 minutes. What is the speed in km/h?

Time Converter (Avoid the Common Trap!)

Convert between decimal hours and hours/minutes.

2.5 hours = 2 hours 30 minutes
Remember: 2.25 hours is NOT 2 hours 25 minutes! It's 2 hours 15 minutes (0.25 � 60 = 15).

Journey Planner Activity

Plan a trip using map distance, scale, and speed.

Click "Plan Journey" to see results

Speed Limit Quiz

Determine if each driver is speeding based on South African speed limits.

Scenario 1: Driver on freeway covers 110 km in 1 hour
Scenario 2: Driver in urban area (60 km/h limit) covers 25 km in 30 minutes
Scenario 3: Driver on rural road (100 km/h limit) covers 85 km in 1 hour
Scenario 4: Driver on freeway covers 150 km in 1 hour 15 minutes

Problem-Solving Framework

1
Map

Find Distance from Map

Measure distance on map. Apply scale to convert to actual distance.

Tip: Measure carefully. For curved roads, use string or measure in segments.
2
Identify

Identify What You Need to Find

Determine whether the question asks for time, speed, or distance.

Questions: Travel time? Required speed? Arrival time? Speed limit compliance?
3
Select

Select the Correct Formula

Time = Distance � Speed, Speed = Distance � Time, Distance = Speed � Time

Formula Tips: Cover the unknown in the triangle. Ensure units match.
4
Calculate

Perform the Calculation

Do the calculation carefully. Time may need conversion to hours/minutes.

Tips: Write down all steps. Convert decimal time to minutes if needed.
5
Interpret

Interpret the Result

Convert answer to practical format. For time, express in hours/minutes.

Tips: "2.5 hours" becomes "2 hours 30 minutes". Add to departure for arrival.

Assessment Focus Areas

Formula Application

Correctly select and apply the appropriate time-speed-distance formula.

Key Skills

  • Identify which formula to use
  • Rearrange formulas correctly
  • Apply to various contexts

Time Conversions

Convert confidently between decimal hours and hours/minutes.

Key Skills

  • Decimal to minutes (�60)
  • Minutes to decimal (�60)
  • Avoid 2.25 = 2h25m mistake

Map Integration

Combine scale calculations with time-speed-distance formulas.

Key Skills

  • Measure map distances accurately
  • Apply scale correctly
  • Integrate with travel calculations

Unit Consistency

Ensure all units match before calculating and convert when necessary.

Key Skills

  • Match km/h with km and hours
  • Convert between km and m
  • Convert between hours and minutes

CAPS Curriculum Requirements

Knowledge and Understanding

  • Understand the relationship between time, speed and distance
  • Know the three formula variations
  • Understand time conversion between decimal and minutes
  • Know South African speed limits for different road types

Skills and Applications

  • Calculate travel time from map distance and speed
  • Determine if a driver is speeding
  • Calculate arrival times from departure times
  • Convert between time formats correctly

Real-World Contexts

  • Trip planning and journey time estimation
  • Speed limit compliance checking
  • Road trip scheduling
  • Interpreting travel data from maps