Math Help Needed

mekki

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Jun 3, 2001
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My brain is not working well and I just can't figure this out. I know I'm supposed to set up some kind of ratio, but that's as far as I can get /ubbthreads/images/graemlins/confused.gif

Here's the problem:
Imagine the following scenario: You are pedaling up a small hill at 12 km/h on your pedal-only bike. During the climb, you are passed by 20 cars travelling at 40 km/h. Now, if you can maintain a speed of 24 km/h up the grade, you are only passed by X cars, and the average passing speed is now only X km/h instead of X km/h!

Not sure about the wording of that last part - is it really the average passing speed I'm talking about or something else? /ubbthreads/images/graemlins/crazy.gif
 

tsg68

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Breukelen, NY established 1646
Homework?!! Sorry I suck at math! /ubbthreads/images/graemlins/tongue.gif /ubbthreads/images/graemlins/wink.gif

Later,
TSG /ubbthreads/images/graemlins/grin.gif
 

flownosaj

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I feel that this is a flawed math problem because it forces you to assume that all these cars are traveling at regular intervals, not all in one "pack" and does not include a time variable.

The first answer to pop into my head would be half as many cars if you double your speed. Average passing speed would be 16 km/hr (40-24)

It's late, I could be wrong /ubbthreads/images/graemlins/smile.gif

-Jason
 

mekki

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Yeah, I think you're right that it is over-simplified, but I think there is some validity to the concept? It is late, so maybe I am just making stuff up /ubbthreads/images/graemlins/frown.gif
 

DieselDave

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Seems straightforward. Throw in the hill length, say you stopped for 40 seconds and then reversed directions 5/8 of the way to the top and were headed towards traffic at 30 km/hr and the traffic came to a complete stop for 15 seconds when you reversed directions plus every 4th car was an EV that ran out of juice going up the hill and every 7th vehicle was a diesel putting out plumes of black smoke that caused you to stop for 3 seconds every time one of them went by and it would get fun.
 

flownosaj

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What about stopping to change batts in your jury-rigged surefire headlight 'cuz your HOLA ate up all your lithiums halfway up the hill. /ubbthreads/images/graemlins/tongue.gif

-Jason
 

immybaby

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Cambridge, UK
Ok here you go:

You are right it's just about ratios. The passing speed when you are going at 12 km/h is 28km/h (40-12), and similarly when you are going at 24 km/h it's 16 km/h.

This means that (using distance/ speed = time)

20/28 = x/16 where x is the number of cars at the increased speed.

so x=16*20/28 = 11.4 cars.
 

whiskypapa3

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It ain't the rocket science I used to do but I'll try to help.

First get rid of the hill, at my age I don't do hills.

Then scale it so the unit 'h' equals 1.

Now we have a 40 km flat road. In one hour you have gone 12 km, and in the remaining 28 km there are the 20 cars that have passed you. That means that the cars are spaced 28/20 = 1.4 km apart.

Your buddy took off at 24 km/h leaving 16 km at the end of the hour and 16/1.4 = 11.42+ cars pass him.

Your other buddy back at the start with a broken chain has had 40/1.4 = 28.57+ cars pass him and the first car (the SAG team in the van) has had 0/1.4 = 0 cars pass him.


Since we had to determine the interval and had no reason not to make it an even distribution the average passing speed = passing speed or in your case 40-12 = 28 km/h, your first buddy 40 -24 = 16km/h.

D = 40 km
Cars1 = 20
D1 = 12 km (12 km/h*1)
D2 = 24 km (24 km/h*1)

Intv = (D - D1)/20

Cars2 = (D - D2) / Intv
 

mekki

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You guys are great! /ubbthreads/images/graemlins/bowdown.gif

I feel like a dolt, but I just couldn't figure out "20/28 = x/16" /ubbthreads/images/graemlins/ohgeez.gif

Thank you for all the help, and whiskypapa3, you could handle the hills no sweat if you just had one of our electric bikes /ubbthreads/images/graemlins/wink.gif
 
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