Constant of variation: Find the speed of each bus.

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evan399

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A local bus travels 16mph slower than the express. If the express travels 91mi in the same time it takes the local to travel 65mi, find the speed of each bus.
 
Re: Constant of variation

evan399 said:
A local bus travels 16mph slower than the express. If the express travels 91mi in the same time it takes the local to travel 65mi, find the speed of each bus.
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Please show your work - indicating exactly where you are stuck.
 
evan399 said:
I don't know where to begin.
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Ah. So your class hasn't covered this topic yet. That's a bit awkward....

We can provide links to lessons, so you can learn enought to get started, but we'll need to know how far back to go. I'm assuming (since you're at least in Intermediate Algebra) that you're okay with variables and solving linear equations. Have you learned how to translate English into math yet? Do you have any experience with uniform-rate exercises, using the "distance equals rate times time" relationship?

Please be specific. Thank you! :D

Eliz.
 
'fraid not.

let r = speed of the express

r - 16 = speed of the local

they both travel the same time t ...

rt = 91

(r - 16)t = 65

you have two equations with two unknowns, solve the system of equations for r, then determine (r - 16).
 
evan399 said:
so what's the next step? Do I plug one equation into the other?
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Okay; let's slow down. You appear to be somewhat-frantically guessing, and you're still not understanding what has been provided to you. That's not good. :shock:

For a start, try studying this web lesson on how to set up and solve "distance" word problems. :idea:

Once you've worked through all of the examples in that lesson, you should be better able to understand how to derive the following, and also how to finish the solution:

. . .local:
. . . . .distance: 65
. . . . .rate: r
. . . . .time: 65/r

. . .express:
. . . . .distance: [copy this value from exercise]
. . . . .rate: r + 16
. . . . .time: ??

Complete the table above, using what you've learned about the "d = rt" equation. Then, since the distances were covered in "the same time", set the two "time" expressions equal to each other, and solve for "r". Back-solve for the speed of the faster bus. :D

Eliz.
 
evan399 said:
So (rt)/(91)=((r-16)(t)/(65))?
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What you've done matches neither of the set-ups you've been given, nor what the lesson in the link taught. You're quite welcome to use your own set-up and reasoning, but you'll need to show how you got to this point.

Please be complete. Thank you! :D

Eliz.
 
I looked at the lesson and I didn't see anything that resembles my problem.
I tried to set up a chart like they did with distance of the local bus being 65 and 91 for the express. r for the local would be r and t for the local would be 65/r. r for the express would be r+16 and t would be ? . So, that being said I still don't know how to set up the equation. Maybe 91(r+16)=t would be the first equation?
 
evan399 said:
I looked at the lesson and I didn't see anything that resembles my problem.
Maybe 91(r+16)=t would be the first equation?
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"The lesson" gives you the formula: speed = distance / time

Your 91(r+16) = t means speed times distance = time:
you are in serious need of classroom help.
 
evan399 said:
Okay, then it should be 91=(r+16)t
would this be one of the equations?
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I'm sorry, but you're more "lost" than an online service such as this is able to help with. Please consider hiring a qualified local tutor, setting aside several hours a week (daily sessions would be best) to spend in intensive re-teaching.

My best wishes to you! :D

Eliz.
 
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