SP1-L31 Speed Practice

(Part 1) TEACHING(10-15mins)                                

1. Time,Writing speed in km/h, m/min, cm/s

2. Rate and Speed

(Part2) PRACTICE (25-40mins)

Start Time:                    End Time:              
For question 1 – 2.
The table below shows the daily payment rates for a restaurant worker. (15/p2/18f)

1. Jim worked from Tuesday to Sunday. How much was he paid?

2. If Jim was paid $110 for working 5 days continuously, which day could he have started to work?

3.  Anna swims 450m in 5 mins. Find her swimming speed in m/min.

4.   The distance between Town A and Town B is 216 km. John rides his car at a speed of 54 km/h. How long will John take to travel from Town A to Town B?

5.  A car travelled at a speed of 60 km/h for 3 ½ h. Find the distance travelled?

6.    Michael cycled at an average speed of 24 km/h. How far did he travel after cycling for 120 minutes? (10/p1/s)

(1) 5km

(2) 12 km

(3) 48 km

(4) 72 km                                                             

7.   Sharon took 10 minutes to cycle from her house to the park which was 3 km away. What was Sharon’s average speed? (18/p1/s)

For question 8 – 9.

John left Town G at 10 00 and drove to Town H at an average speed of 60 km/h. Half an hour later, Ian left Town G and drove to Town H travelling along the same route as John. He met John at a petrol station at 13 00 before reaching Town H at 1400. The petrol station was 10 km from Town H. (13/p2/s

8. Find the distance between Town G and Town H.

9. Find the average speed of Ian for the whole journey. (assuming he did not stop at the petrol station. Give your answer correct to the nearest whole number.)

10.*  A postbox is 450 m from Wendy’s house. Wendy took 10 min to walk from her house to the postbox and back again. what was her average walking speed?
Extra
1.* Tracy took ¾ h to jog 6 km. What was her average jogging speed in km/h?

2.*  Water from a tap leaks at a rate of 15 ml per min. At this rate, how much water is leaked in 2 hours? Give your answer in litres

3.*  Mary and Cindy started cycling at the same time along a 4.5 km track. Both did not change their speeds from start to finish. Mary cycled at 375 m/min. when she reached the end of the track, Cindy was 600 m behind her. What was Cindy’s cycling speed in m/min?

4.*  Danny and Elise started jogging at the same time along the route shown below. Both did not change their speeds throughout. After 35 min, Danny was at the halfway point and Elise was 300 m behind. Danny reached the end point 5 min before Elise. What was the distance of the route?

TheMathbooklets Content Page 
Practice Content Page 

Speed Answer Keys

1.         $140

2.         Tuesday

3.         90 m/min

4.         4 h

5.         210 km

6.         90 m/min

7.         3

8.         190 km

9.         74 km

SP1 Speed/Rate

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)

             

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 ?

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 ~~~~ :)