Tuesday, April 28, 2009

Singapore Math: NYPS 2008 Speed Question

Another Speed question, this one from Nanyang Primary's 2008 Prelim paper (Qn 47).

Lily is meeting a friend at a certain time. If she drives at 80km/h, she will be 1/3 h late. If she drives at 60km/h, she will be 3/4 hour late. How long will the journey take if she drives at 90km/h?

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Brian's working (refined for this post):

At 80km/h or 240km/3h --> 20 min late
At 60km/h or 240km/4h --> 45 min late

Difference in time taken is 1 hr or 60 min per 240km.

60 min --> 240km
25 min --> 25/60 x 240 = 100km

Time taken at 90km/h
--> Distance divided by speed
--> 100km/90km/h = 1 1/9 h

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I worked the solution out by Algebra:

Let D be distance and T be time taken

D / (T + 1/3) = 80
D = 80T + 80/3 ---> (1)
D / (T + 3/4) = 60
D = 60T + 45 ---> (2)

(1) - (2)

20T = 55/3
T = 55/60 ---> (3)

Substitute (3) into (2)

D = 55 + 45 = 100km

When Lily drives 90km/h:

T = D/90 = 100/90 = 1 1/9 hr

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4 comments:

monlim said...

Thanks for this! When you showed me the algebra working, I understood it, but I still can't get Brian's working. I don't know why he found 240km.

Lilian said...

He said he needed to make the distance equal, 240 is the lowest common multiple for 60 and 80.

When he got back from school and I asked him to redo the question, he actually did it another way. This time, he made the difference in the denominator (time) 25 min, ie,

80km/h = 100km/75min
60km/h = 100km/100min

That was how he got 100km. And from there, he calculated the time taken at speed of 90km/h.

Have I confused you more? :P I think I confused myself!

monlim said...

Orrrrr.... aiyah, genius lah! I can't believe he can work all this out WITHOUT having learned any of it in school...

Lilian said...

Genius your head lah.

Actually, I don't even know if the working is acceptable.

When it comes to Singapore math papers, the element of luck comes into play, sometimes he can see it clearly, sometimes easy questions stump him.