D=RT: how far is meeting point from city of Harmony?

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zfrymier

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I'm working on a Pre-Calculus word problem here, and it is making my head spin. Normally I can solve it if I can find what things are equal between the two situations i.e. the rate or time. However, no matter which angle I look at it, I cannot find anything that would be considered equal between the two! Okay, so here is the problem:

"The city of Harmony is 430 miles from the city of DIssension. At 12:00 noon, Paul Haymaker leaves Harmony travelling at 60 miles per hour towards Dissension. One hour later, Nick Ploughman starts from Dissension heading toward Harmony, managing only 45 miles per hour. When will they meet? How far is the meeting point from Harmony?"

Any help would be greatly appreciated!
 
Re: D=RT

You should be able to express each traveler's distance travelled in terms of time and rate. One travels at 60 mph for t hours. The other travels at 45 mph for t-1 hours. The sum of their distances traveled = 430 miles.
 
Re: D=RT

Right, I understand this much. I'm asking how do I figure at what time these two will meet (they are travelling in opposing directions) and how far they will be from Harmony when they do meet.
 
Re: D=RT

If the first guy travels for t hours, and you build an equation in terms of t, when you get the value of t in hours and minutes, just add that to 12:00. I got an answer of 4 hrs 31 min 26 sec after 12:00. To get the distance, you know the rate of the guy traveling from Harmony (which, by the way, is a small town on the central coast of California. I don't know where Dissension is.) so multiply that rate times the time it took him and you get the distance.
 
Re: D=RT

I'm still not understanding where you are getting the 4 and half hours though. For my equation and i'm setting up as: t=430/60? or am I missing something?
 
Re: D=RT

zfrymier said:
I'm working on a Pre-Calculus word problem here, and it is making my head spin. Normally I can solve it if I can find what things are equal between the two situations i.e. the rate or time. However, no matter which angle I look at it, I cannot find anything that would be considered equal between the two! Okay, so here is the problem:

"The city of Harmony is 430 miles from the city of DIssension. At 12:00 noon, Paul Haymaker leaves Harmony travelling at 60 miles per hour towards Dissension. One hour later, Nick Ploughman starts from Dissension heading toward Harmony, managing only 45 miles per hour. When will they meet? How far is the meeting point from Harmony?"

Any help would be greatly appreciated!
Click to expand...

Assume that they meet at a time t hours after 12.

Then Paul traveled for (t * 60) miles - Nick travels (430 - t*60) to meet Paul

Then Nick traveled for (t - 1) hr

So distance traveled by Nick is (t - 1) * 45 which is also (430 - t*60)

Solve for t from above.
 
Re: D=RT

zfrymier said:
I'm still not understanding where you are getting the 4 and half hours though. For my equation and i'm setting up as: t=430/60? or am I missing something?

That t would be correct if Paul had to travel all of 430 miles (at 60 mph) to meet with Nick
Click to expand...
 
Re: D=RT

H......>(Paul-1 pm)..........@60................................>?<................@45..........(Nick-1 pm)D

Since Paul has travelled 1 hour by 1pm, then have them both starting at 1pm, distance left being 430-60 = 370

The 370 miles is being travelled at 60+45 = 105 mph....OK?
Carry on.
 
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