# D=vt problem

## 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?

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

## Answers and Replies

Dick
Science Advisor
Homework Helper
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?

HallsofIvy
Science Advisor
Homework Helper

## 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?

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.

Dick
Science Advisor
Homework Helper
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.

HallsofIvy
Science Advisor
Homework Helper
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!

Avodyne
Science Advisor
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.