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 Post subject: maths challengePosted: Thu Apr 03, 2014 7:17 pm

Joined: Thu Mar 17, 2011 12:58 pm
Posts: 92
Hello!
Any clue on this question... much appreciated.

A motorist drove 240 km. If he had gone 20km/h faster, he could have made this trip in one hour less time. How fast did he drive?
The answer given is 60 km/h but what is the method...?

Thanks

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 Post subject: Re: maths challengePosted: Thu Apr 03, 2014 8:05 pm

Joined: Fri Oct 12, 2007 12:42 pm
Posts: 3804
I would suggest a systematic trial and improvement approach for a 10 yr old.

1 kph = 240 hrs, 10kph = 24 hrs, so 21 nowhere near
240 kph = 1hr. Impossible to be 1hr less
120 kph = 2hr. One hr less would have to be 240kph
80 kph = 3hr, but 100 = 2.4 hrs
60 kph = 4hrs, done.

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 Post subject: Re: maths challengePosted: Thu Apr 03, 2014 8:06 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11740
original time = 240/v where v is the speed

new time = 240/(v + 20)

which is bigger? Well we're told new time is one hour less.

so try that ... will come back with another hint if that doesn't help.

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 Post subject: Re: maths challengePosted: Fri Apr 04, 2014 8:41 am

Joined: Sat Aug 10, 2013 11:46 am
Posts: 168
What age is this aimed at?

My 10 year old solved it by trying out different speeds.

The only way I could find of solving it properly was using quadratics. Is there an easier way of doing it properly using algebra or do you think they want the trial and error approach?

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 Post subject: Re: maths challengePosted: Fri Apr 04, 2014 9:21 am

Joined: Mon Aug 12, 2013 9:13 am
Posts: 452
Not surprised that this is challenge question and geared for year 6/7.

I prefer the long way of doing it.

1. One must know the formula...... Speed = distance over time

2. Convert word problem into numbers/variables
Speed Distance Time
s 240 t
s+20 240 t-1

3. Form equation
s+20 = 240/t-1
s = 240/t

4. Solve simultaneous equation
20 = (240/t-1) - (240/t)

5. Hit n trial
The numbers that question contains are purposely given to ease calculation. The hint lies in the number 240. It is like 24 which comes in times table for 3, 4, 6 and 8.

For t = 4

(240/4-1) - (240/4)
80-60 = 20

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 Post subject: Re: maths challengePosted: Sun Apr 06, 2014 10:12 am

Joined: Tue Feb 05, 2013 10:27 am
Posts: 46
I found trial & error was the easier way for my dd to understand how to tackle this. Where did you see this question?

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 Post subject: Re: maths challengePosted: Sun Apr 06, 2014 11:01 am

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11740
Please can we refer to 'trial and improvement' not 'hit n trial' or 'trial and error'.

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 Post subject: Re: maths challengePosted: Tue Apr 08, 2014 12:47 pm

Joined: Thu Mar 17, 2011 12:58 pm
Posts: 92
Thankyou all for the effort .

It was from maths challenge previous papers!

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 Post subject: Re: maths challengePosted: Tue Apr 08, 2014 8:07 pm

Joined: Wed Jul 31, 2013 4:03 pm
Posts: 1364
Guest55 wrote:
Please can we refer to 'trial and improvement' not 'hit n trial' or 'trial and error'.

DS is always telling me off for calling it 'trial and error' - I'd never heard of 'trial and improvement' before.
Still, the message has got through to him, Guest55

JD

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 Post subject: Re: maths challengePosted: Wed Apr 09, 2014 1:14 pm

Joined: Mon Aug 12, 2013 9:13 am
Posts: 452
Yes, trial and improvement sounds too academic. Good for books but I doubt if children say that. Mine doesn't.

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