Uniform Motion: bus takes 2hr, express takes 45 mins on same

[kraycubs]

A commuter bus takes 2 hours to get downtown; an express bus, averaging 25 mph faster, takes 45 minutes to cover the same route. What is the average speed for the commuter bus?

I have tried to figure this 5 different ways and still can't get it to work. I know the anwere is 15 mph, but don't know how they set up the problem or how they got that answer. All I need help with is setting it up.

x=commuter bus
x+25=express bus
120 minutes
45 minutes

Thank you kindly

 

[tkhunny]

Re: Uniform Motion Word Problem

A commuter bus takes 2 hours to get downtown; an express bus, averaging 25 mph faster, takes 45 minutes to cover the same route. What is the average speed for the commuter bus?

I have tried to figure this 5 different ways and still can't get it to work. I know the anwere is 15 mph, but don't know how they set up the problem or how they got that answer. All I need help with is setting it up.

x=commuter bus
x+25=express bus
120 minutes
45 minutes

Thank you kindly

A couple of things:

1) 2 hrs, 25 mph, 45 min -- Two in hours and one in minutes. Why did you convert two, rather than one? Are you afraid of fractions?

2) Write better definitions: x = Speed of commuter bus in mph, x+25 = Speed of commuter bus in mph,

3) Write out your controling formulations: Distance = Rate * Time

4) Translate any out-of-step information. 45 min = 3/4 hrs

5) Write out all the relationships based on your controlling formulations.

Commuter: Distance = x * 2 hr
Express: Distance = (x+25) * (3/4) hr

Now, can you see how deliberately I am proceeding? Can you see how I am letting the notation and the structure keep it organized for me? This frees my brain to think about what I am doing, rather than just trying to keep everything organized. Can you finish from there?

 

[kraycubs]

Re: Uniform Motion Word Problem

I understand what you are saying. Still not enough info to help set it up. All the other word problems I have, gave me the distance and I was able to complete them without any issues. This one however, still leaves me for a loop. Do you figure the distance or the speed first. Can you put it together or give me a sample?

 

[skeeter]

Re: Uniform Motion Word Problem

let v = average speed of the commuter bus

speed*time = distance

for the commuter bus, v*2 = distance
for the express, (v+25)(3/4) = the same distance

so ...

2v = (v+25)(3/4)

do the algebra and solve for v.

 

[tkhunny]

Re: Uniform Motion Word Problem

I understand what you are saying. Still not enough info to help set it up. All the other word problems I have, gave me the distance and I was able to complete them without any issues. This one however, still leaves me for a loop. Do you figure the distance or the speed first. Can you put it together or give me a sample?

kraycubs!

Look really hard at these two equations.

Commuter: Distance = x * 2 hr
Express: Distance = (x+25) * (3/4) hr

This is ENTIRELY set up. All that is left is to solve it. Just take the final leap.

Hint: Commuter Distance = Express Distance.
Knowing this, what can you say about "x * 2 hr" and "(x+25) * (3/4) hr"?

It's all there. Reach out and grab it!