ACT Problem: Distance, Rate and Time

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Discussion Overview

The discussion revolves around a problem involving distance, rate, and time, specifically how to determine the distance Anthony is ahead of Joan given their respective speeds and the time it takes for Joan to catch up. The focus is on applying the formula d=rt to solve the problem.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Technical explanation

Main Points Raised

  • Joan rides at 15 miles per hour and Anthony at 12 miles per hour, with Joan expected to catch Anthony in 5 hours.
  • One participant questions the interpretation of the d=rt formula, seeking clarification on its meaning.
  • Another participant suggests simplifying the problem by setting Anthony at the origin and adjusting Joan's position accordingly, proposing a relative speed of 3 mph.
  • A different approach is presented where Joan's and Anthony's positions are expressed as functions of time, leading to a mathematical equation to find the distance d.
  • One participant confirms understanding of the d=rt formula, equating it to distance traveled being the product of rate and time.

Areas of Agreement / Disagreement

Participants express different methods for solving the problem, and while some approaches are clarified, there is no consensus on a single solution or method. The discussion remains open-ended with various interpretations of the problem.

Contextual Notes

There are unresolved assumptions regarding the initial positions of Joan and Anthony, as well as the implications of the chosen coordinate system. The mathematical steps presented may depend on specific interpretations of the problem setup.

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Joan is riding her bicycle along a track at 15 miles per hour. Anthony, who is ahead of Joan on the same track, is riding his bicycle at 12 miles per hour. If it will take Joan 5 hours to catch Anthony at their current speeds, how many mile ahead of Joan on the track is Anthony?

How would you solve it using the d=rt formula?
 
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Re: ACT problem

816318 said:
Joan is riding her bicycle along a track at 15 miles per hour. Anthony, who is ahead of Joan on the same track, is riding his bicycle at 12 miles per hour. If it will take Joan 5 hours to catch Anthony at their current speeds, how many mile ahead of Joan on the track is Anthony?

How would you solve it using the d=rt formula?

Hi 816318, could you expand on what you intend the d = rt formula to mean? Maybe i should know from experience.. I'm thinking distance equals something by time.. Ha :p. I'll feel silly when i realize, but we have to know for sure!
 
Re: ACT problem

816318 said:
Joan is riding her bicycle along a track at 15 miles per hour. Anthony, who is ahead of Joan on the same track, is riding his bicycle at 12 miles per hour. If it will take Joan 5 hours to catch Anthony at their current speeds, how many mile ahead of Joan on the track is Anthony?

How would you solve it using the d=rt formula?

We can simplify this problem a bit if we orient our coordinate axis such that Anthony is at the origin and Joan is some distance away approaching the origin at 3 mph. Can you proceed?
 
Re: ACT problem

MarkFL said:
We can simplify this problem a bit if we orient our coordinate axis such that Anthony is at the origin and Joan is some distance away approaching the origin at 3 mph. Can you proceed?

Thanks I got it now, d=3(5) 15!
 
Re: ACT problem

Another approach would be to initially put Joan at the origin and Anthony at $d$. Disnaces are in miles and time in hours. And then:

Joan's position as a function of time is:

$$J(t)=15t$$

Anthony's position as a function of time is:

$$A(t)=12t+d$$

Now, we are told they meet in 5 hours, or:

$$J(5)=A(5)$$

$$15(5)=12(5)+d$$

$$d=15(5)-12(5)=3(5)(5-4)=15$$
 
Re: ACT problem

Joppy said:
Hi 816318, could you expand on what you intend the d = rt formula to mean? Maybe i should know from experience.. I'm thinking distance equals something by time.. Ha :p. I'll feel silly when i realize, but we have to know for sure!
distance traveled= rate of travel times time traveled.

You may know it better as "d= vt" where "v" is now "velocity".
 

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