## Wednesday, 19 April 2017

### Speed: Every Minute Counts...

Enter your individual response in the comment. Remember to label the parts as given.

(1) Describe clearly how would you approach the question?
(2) What is your final answer (round off to 3 SF if it is non-exact)

Duration: 5 minutes

Suggested Train of Thought...
The following suggestion reduces the 'redundant' working (updated on 23 April 2017)

Step 1: Draw out the info available
Speed of Wolf: 65 km/h
Little Red Riding Hood (LRRH) - start 35 minutes later; catch up after 130 km.

Step 2: Make inference
Since distance travelled by both Wolf and LRRH is the same,
then Wolf would have travelled 130 km.

Thinking:
By finding the time taken by Wolf, we can find the time taken by LRRH to travel the same distance (since she started 35 min later).
With this time, we can find the speed that LRRH travels at.

Step 3: Find time taken by Wolf. This will enable us to find amount of time LRRH has taken.
Distance by wolf = 130 km.
and time taken by Wolf = distance ÷ speed = 130 / 65 = 2 hours

Step 4: Find time taken by LRRH
Remember both Wolf and LRRH travel the same distance,
and LRRH started 35 min later than
Since wolf takes 2 hours to cover a distance of 130 km,
Time taken by LRRH = 2 h - 35 min = 85 min
Convert the time to h, we have 1 5/12 h

Step 5: Find speed that LRRH travels at
Speed = Distance ÷ Time
Speed = 130 km ÷ 1 5/12 h = 91.8 km/h (3 significant figures)

1. Lucas:
1)I would find the time taken for the wolf to cover a distance of 130km, then deduct the time before Little Red Riding Rood Started to go along the same route(which is 35min)=85min(time taken for Little Red Riding Hood to reach the wolf)
Now, I will find the average speed . The distance until Little Red Riding Hood caught up with the wolf divided by the time taken for Little Red Riding Hood to reach the wolf gives me the answer

2)1.53(to 3sf)

1. Lucas:
1)I would find the time taken for the wolf to cover a distance of 130km, then deduct the time before Little Red Riding Rood Started to go along the same route(which is 35min)=85min(time taken for Little Red Riding Hood to reach the wolf)
Now, I will find the average speed . The distance until Little Red Riding Hood caught up with the wolf divided by the time taken for Little Red Riding Hood to reach the wolf gives me the answer

2)91.8km/h(to 3sf)

2. Lucas,
Your 2nd response is correct :)
It would be better if you had mentioned converting 85min to hour since the unit of speed we are working on is km/h.

2. 1) 1st: Find out how far the wolf travelled in 35 min.
2nd: Take Little Red Riding Hood's distance minus the wolf's distance travelled in 35 min.
3rd: Take the wolf's distance travelled and divide it by its speed.
4th: Take Little Red Hood's distance divided by the time to get the final answer.

2) 91.743km/h (3SF)

1. 2) 91.8km/h (3SF)

2. Matthew,
Please elaborate what are you trying to establish in steps 2 to steps 4.

Point to Ponder:
1. What do we need to find?
2. Using the formula, distance = speed x time, what info we do need in order to find the answer?

3. 1) I will first find out how much the wolf has travelled
2) Then I will take Red Riding Hood's distance left subtract the wolf's distance covered
3) Then have the wolf travelled distance divided by its speed
4) Then take the Red Riding Hood's distance over by the time taken to get the answer

Q2) 75.8km/h

1. Its 91.8(3sf)

2. Rui Yang

The distance that the wolf has travelled - isn't it same as little red riding hood's distance?
What are you trying to establish in Step 3?

Note: Answer - unit is missing.

4. Question 1:
1) Firstly, I would find out the distance covered by the woof in 35mins
2) Secondly, I would subtract the total distance Red Riding Hood travelled to catch up with the woof by the distance covered by the woof in 35mins.
3) Thirdly, I would find the time the woof takes to travel 1105/12 km (The answer in part 2)
4) Fourthly, I would find the speed of Red Riding Hood by dividing 130km (The total distance Red Riding Hood covered) by the time taken for the woof to cover 1105/12 km.

Question 2:
91.8km/h (3 SF)

5. Qn 1
1)Change 35 mins into hours
2)Find the distance covered by the wolf for the first 35 mins
3)Take 130 minus that distance to find D
4)Find the time taken for the wolf to travel D
5)That is the total time Red Riding takes to catch up with the wolf
6)To find the average speed, take the total distance(130km) divided by the total time taken in (5)
As I go through the steps, I record it on a timeline to make it clearer to see
Qn 2
91.8km/h (3SF)

6. Q1
1) I would draw 2 timelines one on top of the other, both of equal lengths
2) Label the top timeline "wolf" and the bottom timeline "red riding hood"
3) next i would arrow out the extra space on the first timeline, put 35 minutes converted to 7/12 hrs
4) I would find out how much distance was covered in that 7/12 hrs (7/12 x 65 )
5) next, would arrow out the whole bottom timeline and label it 130km, which is also the same length as the top timeline.
6) i take 130 - 37 11/12 = 92 1/12
7) I take the answer at step 6 and divide it by 65 which gives me 1 5/12
8) answer at step 7 is the amount of time that Red riding hood took to travel the 130 km , so i can use 130 to divide by 1 5/12 which will give me the answer of red riding hood's speed

Q2
91.8 km/h (3 SF)

7. This comment has been removed by the author.

8. 1)Find the distance that the wolf travelled in 35 minuets which is 35 min x 65km/h=37.9km (3s.f).
2)Find the distance the wolf after the his plan got foiled which is 130km-37.9km=94.1 km
3)Use the distance found in 2) and divide it by the average speed to get find the time it takes for Little Red Riding Hood to travel 130km, which is 94.1km divide by 65km/h=1.45 h (3s.f)
4) The answer in 3) is the time Little red Riding Hood takes to travel 130 km, so to find her average speed, take 130km divide by 1.45 h= 89.7 km/h(3s.f)

9. 1) Find out the time the Wolf took until he met Little Red Riding Hood :
130km/ 65km/h = 2h

2) Find the time Little Red Riding Hood took till she met the Wolf :
2h = 120 min
120 min - 35 min = 85 min

3) Find the speed of Little Red Riding Hood:
130km/ 85 min x 60 min = 91.8km/h (3s.f)

10. Question 1
1)Convert 35 mins into hours to find the distance covered by the wolf in the 35 minutes by multiplying that number by the speed at which the wolf was travelling at
2) subtract that distance from 130(d travelled by Red Riding Hood)
3) divide the speed of the wolf by the distance in 2 to find how long Red Riding Hood took to catch up with the wolf
4)Divide the total distance by the total time taken in 3

Question 2
91.8km/h (3SF)

11. Q1.
1) I would find the distance covered by the Wolf has travelled in 35 mins (65 km/h X 35/60 h = 37 11/12 km)
2) Calculate the distance covered by the Wolf after the first 35 mins (130 km-37 11/12 km = 92 1/12 km)
3) Find the time taken for the Wolf to travel 92 1/12 km.(92 1/12 km divided by 65 km/h = 1 5/12 h)
4) Find the speed of Little Red Riding Hood with the distance(130 km) and time taken (1 5/12 h) (130km divided by 1 5/12 h = 91 13/17 km/h)

Q2.
Ans= 91.8 km/h (3 S.F.)

12. Qn1:
Find distance covered by Wolf that has travelled in 35 mins:
65 km/h X 35/60h = 37 11/12 km
Calculate distance covered by Wolf after 35 mins :
130 km-37 11/12 km = 92 1/12 km
Find the time taken for the Wolf to travel 92 1/12 km
(92 1/12 km/65 km/h = 1 5/12 h)
Find the speed of Little Red Riding Hood with the distance
130 km
Find time taken
(1 5/12 h)
Speed of Little Red Riding Hood:
130km divided by 1 5/12 h = 91.8km/h (3sf)

Qn2: 91.8km/h (3sf)

13. First of all, I would find the total time taken for the wolf to travel from judging by his speed which is 2h=120 minutes
Next, I would take 120 min and minus 35 min and you will get 85 min which shows the amount of time taken for little red riding hood to travel for 130 km
lastly, take 85 min and divide the 130 km and you will get 91.8km/h (3sf)

14. 1) Convert 35mins to hours.
35min/60min = 7hours/12hours
2) Find the distance travelled by the wolf
65 * 7/12 = 37 11/12
3) Subtract the distance travelled by the wolf from 130.
130 - 37 11/12 = 92 1/12
4) Divide the amount by 65 to find the time taken for Red Riding Hood to travel.
92 1/12 / 65 =1 5/12
5) Divide 130 by 1 5/12 to find the speed of Red Riding Hood.
130 / 1 5/12 = 91.764...
= 91.8 km/h (3 s.f) (ans)

15. Qn 1:
1) Convert 35min to hours
35min=35/60 hours
=7/12 hours
2) Find the distance travelled by the wolf in the 35 min
Distance = Speed * Time
= 65km/h * 7/12h
= 37 11/12 km
3) Subtract 37 11/12 km from 130km
130km - 37 11/12 km = 92 1/12km
4) Divide 92 1/12km by 65km/h to find the time taken for Red Riding Hood to travel
92 1/12km / 65km/h = 1 5/12h

5) Divide the distance travelled which is 130km by 1 5/12h to find the speed Red Riding Hood travelled at
130km / 1 5/12h = 91 13/17 km/h

Qn 2:
Ans: 91.8 km/h

1. Sara

Your response is correct, and you have highlighted important things like ensuring the quantity is converted to the correct unit before manipulation. Good.

You have broken down the distance into 2 parts.

Point to Ponder:
- Distance travelled by Little Red Riding Hood (LRRH) would be same as the Wolf.
- Is it possible to find the time taken by the wolf?
- With time taken by the wolf, are you able to find the time taken by LRRH, and eventually the answer?

16. Question 1:

1) Firstly, I would find the distance travelled by the wolf 35 minutes later knowing that the wolf travels at 65km/h. Since 35 minutes = 7/12 hours, Distance travelled by the wolf in 35 minutes will be
7/12 * 65 = 37 11/12 km (Distance = Speed * Time)
2) Secondly, I subtract 37 11/12 km from 130km, which gives me 92 1/12 km.
3) To find the time that Little Red Riding Hood took to travel, we divide 92 1/12 km by 65 km/h, which gives me 1 5/12 h. (Time = Distance/Speed)
4) Now to find the average speed Little Red Riding Hood is travelling at, we divide 130km by 1 5/12h, which gives us 91.8 km/h in 3sf. (Average speed = Total Distance/Total Time)

Question 2:
91.8km/h.

1. Hanafi,