Find Terry's Running Speed | D=vt Problem Solution

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Homework Help Overview

The problem involves determining Terry's running speed based on the relationship between distance, speed, and time. It states that if Terry had run 2.0 km/h faster, he would have taken 30 minutes less to cover a distance of 25 km.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of equations based on the distance formula d=vt, with some attempting to define variables clearly while others question the initial assumptions made about those variables.

Discussion Status

There is ongoing dialogue about the correct interpretation of the variables involved and the formulation of equations. Some participants have provided guidance on how to approach solving the equations, while others have expressed differing views on the clarity of the variable definitions.

Contextual Notes

Participants note the importance of defining variables clearly, particularly in the context of physics problems, and express concerns about the potential confusion arising from undefined variables.

petuniac
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Homework Statement



If Terry had run 2.0 km/h faster, he would have taken 30 minutes less to cover a 25 km run. What was Terry's running speed?

Homework Equations



d=vt

The Attempt at a Solution



equation 1

25 = xy

equation 2

25 = (x +2)(y-0.5)

? Is this right? assuming x = his speed and y = his time
 
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Pretty bad. No offense. Solve your equation for t. So t=d/v. Suppose t1 is the time he would take to run at the original speed v, so t1=d/v. If he'd run 2km/hr faster his speed would be v+2km/hr. So the new time is t2=d/(v+2km/hr). What's t1-t2? Read the problem statement. Can you solve for v?
 
petuniac said:

Homework Statement



If Terry had run 2.0 km/h faster, he would have taken 30 minutes less to cover a 25 km run. What was Terry's running speed?

Homework Equations



d=vt

The Attempt at a Solution



equation 1

25 = xy

equation 2

25 = (x +2)(y-0.5)

? Is this right? assuming x = his speed and y = his time

I disagree with Dick, I think what you have done so far is pretty good. I think it would be a good idea to say at the beginning exactly what x and y are: "x= speed (in km/min) and y= time (in min) required to run 25 km initially". Then you have, as you say, xy= 25.

Now, "If Terry had run 2.0 km/h faster, he would have taken 30 minutes less to cover a 25 km run", so (x+ 2)(y- 30)= 25, as you say. You now have two equations to solve for the two unknown values. Since you are asked only for his speed, x, you might eliminate y from the equations. From xy= 25, y= 25/x so your second equation becomes (x+ 2)((25/x)-30)= 25. If you multiply both sides of that equation by x, you get a quadratic equation to solve for x.
 
I agree with Halls. I think Dick must have been confused about what x and y meant.
 
Yeah well some students feel the urge to use the variables x and y because that's what they use all the time in math. The problem is that in physics using variables that don't suggest what quantities they are make solutions difficult to read. Most especially if they are undefined. If my students (and some of them have) use x and y everywhere without defining them on a test problem, I just mark them wrong.

Next year I'm going to make them explicitly define all variables (and label them uniquely) and assign their numerical values with correct units upon penalty of death! If there is anything that I learned from this past year is that the students that can't even get started on a problem were the ones that didn't do that step correctly or at all.

Sorry rant over.
 
DavidWhitbeck said:
Next year I'm going to make them explicitly define all variables (and label them uniquely) and assign their numerical values with correct units upon penalty of death! If there is anything that I learned from this past year is that the students that can't even get started on a problem were the ones that didn't do that step correctly or at all.

Sorry rant over.
Amen, brother!
 
DavidWhitbeck said:
Next year I'm going to make them explicitly define all variables (and label them uniquely) and assign their numerical values with correct units upon penalty of death!
You'd better call the local morgue now.
 

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