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#1 2007-02-03 19:34:24

manmath
Member
Registered: 2007-02-03
Posts: 2

finding the y intercept

Hello everyone! I'm new here, and from what Ive seen this site will be able to help me get a passing mark for Math year!!

I've come across a problem which I'm really unsure about. and I was wondering if you guys could help me out here! big_smile

4) A group of hikers is to travel (x) km by bus at an average speed of 48 km/h to an unknown destination. They then plan to walk back along the same route at an average speed of 4.8km/h and to arrive back 24 hours after setting out in the bus. If they allow 2 h for lunch and rest, how far must the bus take them?

So, My problem is, I've completely forgotten how I might go about rewriting this situation as a set of linear equations (which is what I am almost certain I need to do!)

I've worked out that m (gradient) would be 48 (as m = rise over run, which just so happens that with my distance versus time graph (I seem to be using) km over time looks exactly the same) - So, according to me, m = 48..

I also know that x is just x, isn't it?? but how do I find out that Y intercept??? I've looked all over the place and cannot find out!!

anyways, thanks for listening, any insight to this would be greatly appreciated.

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#2 2007-02-03 23:16:29

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: finding the y intercept

I think, instead of a set of linear equations, you actually want just one.

The hikers want to take 24 hours to do everything. They need to take the bus to this unknown destination (which will take x/48 hours), walk back to their starting point (which will take x/4.8 hours) and rest (which takes 2 hours).

So the equation is x/48 + x/4.8 + 2 = 24.

Multiply everything by 48: x + 10x + 96 = 1152
Simplify: 11x = 1056
Solve: x = 96km.

And to check, that would mean that it takes 96/48=2 hours on the bus, 96/4.8=20 hours to walk back and 2 hours for rest. 2+20+2 = 24.


Why did the vector cross the road?
It wanted to be normal.

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#3 2007-02-04 23:29:21

manmath
Member
Registered: 2007-02-03
Posts: 2

Re: finding the y intercept

woah!!! I see now! thankyou so much!!

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