Time taken: Duration
~ starting time till the ending time of an event or task.
We can use hours(h), minutes(min) or seconds(s) to measure time taken.
Using hours: the time taken to travel from Singapore to KL by car is 4 hours 39 mins.
(or 279 mins or 16740 seconds)
(or 279 mins or 16740 seconds)
DISTANCE
The length of a specific path traveled between two points.
Distance XY is 5km, X is one point and Y is one point
SPEED
How fast something is moving / Distance covered per unit of time
12 km
Walking Speed = 4km/h, Distance covered per hour is 4km
4km (1hr) 4km (1 hr) 4km (1hr)
Cycling Speed = 6km/h, distance covered per hour is 6km
6km (1hr) 6km (1 hr)
Cycling is faster than walking because it takes less time than walking.
DISTANCE, TIME and SPEED (Rate)
Distance is equal to how much length(distance) that can be covered at a specific speed and time given.
Distance(D) = Speed (S) x Time (T)
Speed = Distance / Time
Time = Distance / Speed
Example:
What is the speed of Usain Bolt for the 100m race?
Method
Step1: Circle/Underline Keywords. Draw the DST triangle
Step2: Fill in the given values.
Distance = 100m
Time = 9.81s
Step3: Solve: Compute the required value
Speed = Distance / Time
= 100 /9.81
~ 10.2 m/s
=> He runs 10.2 m in 1 second
Example
Sunny walked from his home to school, which is 0.8 km away, at an average speed of 50m/min. How many minutes did Sunny take to walk from his home to school ?
Step1: Circle/Underline Keywords. Draw the DST triangle
Step2: Fill in the given values. Convert to required unit (if need be)
[Change km to m]
Distance = 0.8km
“Distance Converter” km(1) : m(1000) : cm(100) -> x
0.8km = 0.8 x 1000 = 800m
Time = 50m/min
Step3: Solve: Compute the required value
Time = Distance / Speed
= 800 / 50
= 16 mins
INVOLVING ONE OBJECT
Example:
At 1pm, Mary started cycling at 20 km/h from her home to the shopping centre, 10 km away. She was at the shopping centre for 2 ½ h.
(a) What time did she leave the shopping centre?
Method
Step1: Circle/Underline Keywords. Draw the Distance line with all the details
Start T=1pm D = 10km Time taken = 2h 10min End T=?
Speed = 20km/h
Step2: Value Required? End Time. Unit ok? Draw/Write DST
[Required: Time, Convert = No], T = D/S
Time = dist / speed = 10/20 = ½ h
Step3: Solve: Answer the question
Time cycle + shopping centre = ½h + 2½h = 3h
She leaves the shopping centre at 1 + 3 = 4pm
Travelling with RESTING TIME
Example
Paul travelled from Town X to Town Z, 270km apart. He took 2 ½ h to drive from Town X to Town Y. He rested for 30minutes and continue driving for 1h 20 min from Town Y to Town Z. Find the average speed that Paul travelled.
Method
Step1: Circle/Underline Keywords. Draw Distance line with all the details
T1 = 2½h T2(rest) = ½h T3 = 1h 20min
D = 275km
Speed = ?
Step2: Value/DST Required? Unit ok? Draw/Write DST
[Required: Average speed, Convert = Yes]
Convert: 30 mins = ½ h
Speed = Total distance / Total time taken
Convert 30 mins = ½ h
Total time = 2 ½ h + ½ h + 1 ½ h = 4 ½ h
Average speed = 270 / 4 ½ h = 60km/h
Step3: Solve: Answer the question
Average speed = 270 / 4 ½ h = 60km/h
Paul’s average speed is 60km/h
NOTE:
(1) RESTING TIME MUST BE INCLUDED WHEN CALCULATING TOTAL TIME.
(2) SAME UNIT OF MEASUREMENTS MUST BE USED IN THE CALCULATION.
SAME DISTANCE
Example
Ali cycles from home to school at 6m/s, and back home at 10m/s. What is his average speed?
Step1: Circle/Underline Keywords. Draw Distance line with all the details
D1 = D2
Step2: Value Required? Unit ok? Draw/Write DST
[Required: Average speed, Convert = No] D = S x T
Distance is the same -> 6 x s1 = 10 x s2
- > s1 = 10, s2 = 6
Average speed = total distance / total time
= 6x10 + 6x10 / 16
Step3: Solve: Answer the question
Average speed = 120/16
Ali’s average speed is 7.5km/h
INVOLVING TWO OBJECTS
TRAVEL IN OPPOSITE DIRECTION
Distance covered = Distance covered by CAR + Distance covered by LORRY
Speed = Total speed of both object
Example:
A car travels from Town A to TownB at a speed of 65km/h while a lorry travels from Town B to Town A at 60km/h. Distance from Town A to Town B is 250km. Both set off at 2pm. At what time do they meet?
Method
Step1: Circle/Underline Keywords. Draw Distance line with all the details
Step2: Value Required? Unit ok? Draw/Write DST
Required: Time they meet=> time taken, Convert: No
Time taken = Distance / speed
= 250 / (65 + 60) = 2 h
Step3: Solve: Answer the question
They meet at 2 + 2 = 4pm
Example
Gary and James started walking from the same place in opposite directions along a straight road. They walked for 50 minutes. At the end of the walk, they were 10km apart. Gary’s average speed was 7km/h. What was James’ average speed?
Method
Step1: Circle/Underline Keywords. Draw Distance line with all the details
Step2: Value Required? Unit ok? Draw/Write DST
Required: James speed, Convert: yes,
50 mins = 50/60 = 5/6 h
Speed = Total Distance / Total time
= 10 / 5/6 = 12 km/h
Step3: Solve: Answer the question
James speed + Gary speed = 12 km/h
James average speed = 12 – Gary average speed
= 12 – 7 = 5 km/h
TRAVEL in The SAME DIRECTION
Example
John and Albert ran In a race. When Albert had completed the race, John had only run
of the distance. Albert’s speed was 75m/min faster than John’s speed. Both of them did not change their speed throughout the race. What was John’s speed in m/min ?
John and Albert ran In a race. When Albert had completed the race, John had only run
of the distance. Albert’s speed was 75m/min faster than John’s speed. Both of them did not change their speed throughout the race. What was John’s speed in m/min ?
Method
Step1: Circle/Underline Keywords. Draw Distance line with all the details
Step2: Value Required? Unit ok? Draw/Write DST
Required: John speed, Convert: No, X = Albert’s speed
Speed = Total Distance / Total time
At the time when Albert completes the race,
Albert John
Speed X X + 75
Time same same
Dist 5/8 of total 1 (Total)
Step3: Solve: Answer the question
Using ratio
8/5 X = X + 75
3/5 X = 75
X = 75 x 5/3 = 125 m / min
John speed is 125 m / min
~~~~ END ~~~~ :)
~~~~ END ~~~~ :)
