My Math Forum Speed problem

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 October 28th, 2009, 11:29 AM #1 Member   Joined: Oct 2009 Posts: 39 Thanks: 0 Speed problem I am not sure this problem belong to this section or not, but here it goes. I have been trying to solve this for a while. A bicyclist makes a daily ride of 40 miles at a constant speed. If he trains hard, he can increase his speed by 4 miles per hour, which would result in a half-hour decrease in time. Find his new speed. I tried many ways. One was to set up a table like this V T D -------------------------------------------- v t 40 --------------------------------------- v+4 t-.5 40 But we still have 2 variables to solve??? Are we suppose to guess for one of the variable???? Any help is appriciated. Thank you.
October 28th, 2009, 05:36 PM   #2
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Re: Speed problem

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 Originally Posted by alikn I am not sure this problem belong to this section or not, but here it goes. I have been trying to solve this for a while. A bicyclist makes a daily ride of 40 miles at a constant speed. If he trains hard, he can increase his speed by 4 miles per hour, which would result in a half-hour decrease in time. Find his new speed. I tried many ways. One was to set up a table like this V T D -------------------------------------------- v t 40 --------------------------------------- v+4 t-.5 40 But we still have 2 variables to solve??? Are we suppose to guess for one of the variable???? Any help is appriciated. Thank you.
You can set it up as 2 equations in 2 unknowns. Let v be the original speed and t the original time.

Start equation 40=vt
End equation 40=(v+4)(t-.5)=vt+4t-.5v-2. This leads to 4t-.5v=2.

Combine with first equation gives a quadratic in either t or v which can be solved.

This is an elementary algebra problem and should be in that section.

 October 30th, 2009, 09:40 AM #3 Member   Joined: Oct 2009 Posts: 39 Thanks: 0 Re: Speed problem Thank you mathman. Do I need move this to elementary algebra section?
October 30th, 2009, 04:53 PM   #4
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Re: Speed problem

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 Originally Posted by alikn Thank you mathman. Do I need move this to elementary algebra section?
Leave that to the people running the forum.

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