maths challenge

[rejim2]

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

[moved]

I would suggest a systematic trial and improvement approach for a 10 yr old.
Start with the factors of 240.

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.

[Guest55]

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.

[russet]

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?

[parent2013]

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

[Reh]

I found trial & error was the easier way for my dd to understand how to tackle this. Where did you see this question?

[Guest55]

Please can we refer to 'trial and improvement' not 'hit n trial' or 'trial and error'.

[rejim2]

Thankyou all for the effort .

It was from maths challenge previous papers!

[JamesDean]

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

[parent2013]

Yes, trial and improvement sounds too academic. Good for books but I doubt if children say that. Mine doesn't.