Q&A - PSLE Math
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Hi Dharma and James Ang
About the speed question, I don’t understand why there must be a relationship between the speed of uphill, downhill and ground level. This is how I teach my ds how to solve the problem. Please let me know if I am wrong. Thanks.
speed ratio UH: DH : GL ---- 4 : 12 : 6
time ratio
(inversely proportional) UH : DH : GL ---- 12 : 4 : 6 ---- 6:2:3 (11u)
total time 2h 20min—7/3 h
11u — 7/3h 1u — 7/33 h
UH distance ---- 6 x 7/33 x 4 — 168/33 km
DH distance ---- 2 x 7/33 x 12 ---- 168/33 km
GL distance ---- 3 x 7/33 x 6 ----126/33 km
total distance ----- 168/33 + 168/33 + 126/33 ---- 14 km -
Hi kancheongmum
I think this question is from a Sec One textbook by Shinglee publishing.
There are three types of terrains, uphill, downhill and level ground.
The point to note is if the cyclist moves uphill in one direction, on the way back he moves downhill. So what is the average speed for this part of the road?
Use common multiple to find the average speed.
uphill ----4, downhill ----12, multiple-----12 (use 12 as the distance)
Distance/Speed ----Time
12/12 ----1h
12/4 ------3h
Average speed ------24/4 ------6 (distance two ways ----(12*2) --24)
Average speed for level ground -------6
Given time ------2h 20mins ------ 7/3h
Applying Distance -----S*T which is taught in P6 Maths
Distance ----7/3*6 -----14km
Best wishes -
I like this method, but Dharma has rightly pointed out that the correct answer should be independent of the distance travelled uphill/downhill.
kancheongmum:
Hi Dharma and James Ang
About the speed question, I don't understand why there must be a relationship between the speed of uphill, downhill and ground level. This is how I teach my ds how to solve the problem. Please let me know if I am wrong. Thanks.
speed ratio UH: DH : GL ---- 4 : 12 : 6
time ratio
(inversely proportional) UH : DH : GL ---- 12 : 4 : 6 ---- 6:2:3 (11u)
total time 2h 20min---7/3 h
11u --- 7/3h 1u --- 7/33 h
UH distance ---- 6 x 7/33 x 4 --- 168/33 km
DH distance ---- 2 x 7/33 x 12 ---- 168/33 km
GL distance ---- 3 x 7/33 x 6 ----126/33 km
total distance ----- 168/33 + 168/33 + 126/33 ---- 14 km -
Hi tianzhu
Thank you for your reply and clear explanation. Now I fully understand the problem. Don’t know why this average thing did not cross my mind. Mental block. Actually this time inversely proportional to speed concept is from the book Conquer Problem Sums for Pri 6 thinking Maths onSponge which my ds use in his school as supplementary material. -
Hi kancheongmum
You’re welcome.
Best wishes -
kancheongmum:
Hi Dharma and James Ang
About the speed question, I don't understand why there must be a relationship between the speed of uphill, downhill and ground level. This is how I teach my ds how to solve the problem. Please let me know if I am wrong. Thanks.
speed ratio UH: DH : GL ---- 4 : 12 : 6
time ratio
(inversely proportional) UH : DH : GL ---- 12 : 4 : 6 ---- 6:2:3 (11u)
total time 2h 20min---7/3 h
11u --- 7/3h 1u --- 7/33 h
UH distance ---- 6 x 7/33 x 4 --- 168/33 km
DH distance ---- 2 x 7/33 x 12 ---- 168/33 km
GL distance ---- 3 x 7/33 x 6 ----126/33 km
total distance ----- 168/33 + 168/33 + 126/33 ---- 14 km
Hi kancheongmum,
Sorry for the late reply. Your method gives the correct answer but the approach in my opinion does not seem to be very correct . If you look at your working, you had worked out the individual distances for uphill , downhill and on level ground. Your workings suggest the distance uphill and downhill are the same but the question is silent about the ratio of individual distances. Since total time is given, it is possible to get the correct answer.
Pls correct me if I am wrong. -
kancheongmum:
Hi kancheongmum,Hi Dharma and James Ang
About the speed question, I don't understand why there must be a relationship between the speed of uphill, downhill and ground level. This is how I teach my ds how to solve the problem. Please let me know if I am wrong. Thanks.
What I meant abt the relationship betw Uphill, downhill Level speeds is that as Tianzhu has shown the average speed of the 3 portions is the same 6km/h and thus the average speed of the whole journey can be taken as 6km/h too. Thus makes life easy as we just need to multiply with the total time taken to find the total distance.
If the average speed on the slope (up and down) and the level ground are different, we have a problem.... -
Dharma, you are right, the speed ratio is inverse of time ratio method/concept has to assume that distance is the same for all 3 uphill, downhill, level components before it can be applied. In the question, the average speed of the uphill/downhill is the same as the level ground speed, so it is independent of distance travelled uphill/downhill. The entire distance can be level or entire distance can be uphill/downhill then back to level ground at the end, the total distance is still 14km. Thanks for pointing that out.
Dharma:
kancheongmum:
Hi Dharma and James Ang
About the speed question, I don't understand why there must be a relationship between the speed of uphill, downhill and ground level. This is how I teach my ds how to solve the problem. Please let me know if I am wrong. Thanks.
speed ratio UH: DH : GL ---- 4 : 12 : 6
time ratio
(inversely proportional) UH : DH : GL ---- 12 : 4 : 6 ---- 6:2:3 (11u)
total time 2h 20min---7/3 h
11u --- 7/3h 1u --- 7/33 h
UH distance ---- 6 x 7/33 x 4 --- 168/33 km
DH distance ---- 2 x 7/33 x 12 ---- 168/33 km
GL distance ---- 3 x 7/33 x 6 ----126/33 km
total distance ----- 168/33 + 168/33 + 126/33 ---- 14 km
Hi kancheongmum,
Sorry for the late reply. Your method gives the correct answer but the approach in my opinion does not seem to be very correct . If you look at your working, you had worked out the individual distances for uphill , downhill and on level ground. Your workings suggest the distance uphill and downhill are the same but the question is silent about the ratio of individual distances. Since total time is given, it is possible to get the correct answer.
Pls correct me if I am wrong. -
kancheongmum:
HiHi all
ai yo after reading the hamster and speed questions send my head spinning. My ds is not strong in this area. Please advise if I should show him these type of questions or just concentrate on the basic concepts which I am doing now. tks
Suggest you get a set of 2010 P6 preliminary testpapers(available from vendors in Sep) to practise before PSLE.
Best wishes -
Hi Dharma
You may find this article on Fibonacci sequence interesting.
http://www.mathacademy.com/pr/prime/articles/fibonac/index.asp
How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?
Enjoy your reading.
Best wishes
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