Maths Problem!

[BertieButton]

Been absolute yonks since I've done any maths and was given this recently but am completely stuck!! Embarrassed to say, that this is a primary school question!!

[fiction-factory]

Tough one, i agree.

[jim360]

You might want to include the problem, too.

[fiction-factory]

If you post the question though we'll have a go.

[BertieButton]

Jonas travels 26 miles in 3 hours, partly on foot and partly on bike. He walks at 4 mph and cycles at 12mph. For what length of time does Jonas walk? How far does he cycle?

[BertieButton]

Apologies! My tablet can't cope with all the adverts on answerbank and goes into meltdown!!

[10ClarionSt]

If this is a primary school question, I think it's a mistake. Seems more like a simultaneous equation to me, but I'm definitely no expert.

[roslyn251254]

walks 5 miles 1 hr 15 mins
cycles 21 miles 1 hr 45 mins

[fiction-factory]

Cycles for 1.75 hours (21 miles) , walks for 1.25 hours (5 miles)

[BertieButton]

Cheers Roslyn +F.F.!
How is it done? Is it an equation??

[jim360]

Don't be embarrassed at not solving that problem: if you're out of practice then it's probably not at all obvious what to do. Right now I'm way too tired to think properly, too.

Maybe a trial-and-error approach is the most intuitive way to solve it. If Jonas cycled for two hours and walked the rest of the time then he'd have travelled (12 x 2) + 4 = 28 miles, so that's just a little too long. If he cycled one hour and walked two hours then he'd have done 12 + (4 x 2) = 20 miles instead.

Next you can try one-and-a-half hours, for a total journey length of (12 x 1.5) + (4x1.5) = 18 + 6 = 24 miles. Still too short, so go half-way again: 12 x (one and 3/4) + 4 x (1 and 1/4) = 21 + 5 = 26.

That works! There are clearly more mathematical solutions, but guesswork can anyway help you get into the problem and is maybe easier to have a handle on.

So anyway Jonas was walking for one-and-a-quarter hours and cycled 21 miles.

[roslyn251254]

equations could be used ? primary school? but like jim360 i just tried a few answers ..didn't take long

[fiction-factory]

Trial and improvement/iteration works pretty well.
Try 2 hours cycling, 1 hour walking- that's 28 miles.
Try 1.5 hours cycling, 1.5 walking- 12x1.5 +4x1.5 =24 miles

Split the difference and check that- gives 26 miles

[fiction-factory]

Shoud have waited to see if Jim replied before typing mine

[BertieButton]

Crikey! Here's me thinking I need Venn diagrams, a graph chart and Pythagoras' theory and it's process of elimination??? Thank you all, I'd have never got this!! Have a beautiful day!

[barmy]

solve 2 equations

4x + 3 y = 26 and x + y = 3 to get x and y

[JJ109]

I would also do it by trial and error, but If you want to do it by solving simultaneous equations, then
Let x = the distance walked and Let y = the distance cycled
Obviously x + y = 26
Second equation x/4 + y/12 = 3 hours
Get rid of the fractions by multiplying everything by 12
Equation 2 becomes
3x + y = 36

Therefore solve
3x + y = 36
x + y = 26
Subtract bottom from top
2x = 10
x = 5
As x + y = 26 and x = 5, it follows that y = 21

This gives the answer which you already know is correct