1. Aug 25, 2007

megaforcetkd

1. The problem statement, all variables and given/known data

A car averages 80 km/h travelling from A to B, and then on the return trip the car averages 60 km/h from B to A. Write the average speed of the car, V, as a function of x, where x is the distance from A to B.

2. Relevant equations

Not sure what to use.

3. The attempt at a solution

Vavg = [80 km/h(x) + 60 km(x)]/2

Obviously it's wrong =/

2. Aug 25, 2007

Leong

you must understand that the average speed in this context means the total distance divided by the time taken to cover that distance.
the average speed here doesn't mean the arithmetic mean that we usually learn in mathematics.

3. Aug 25, 2007

megaforcetkd

The question doesn't provide the time though, and the function needs to be writen as a function of the distance.

4. Aug 25, 2007

Leong

speed = distance/time
you know the average speed for the go and return journeys and the distance is the same. so you can express the TOTAL time to cover both the journeys in term of the distance x.

Last edited: Aug 25, 2007
5. Aug 25, 2007

HallsofIvy

Staff Emeritus
speed= distance/time=> time= distance/speed

Of course, the total distance is 2x.

6. Aug 25, 2007

megaforcetkd

I have to express it as V(x) though so I have to express Speed in terms of distance. This is for Pre-Calc, btw. I did all the mechanics things in AP Physics but this is unrelated, right? I've been trying for a while but I still can't get it =/..

I know I can express it in terms of time as T = ((x)/(80kph)) + ((x)/60kph))..

7. Aug 25, 2007

learningphysics

That's right. That's the total time for the trip. What's the total distance in terms of x?

8. Aug 25, 2007

megaforcetkd

2x = ((x)/(80kph)) + ((x)/60kph))(speed).. what do i put for speed?

9. Aug 25, 2007

learningphysics

Solve this expression for speed.

10. Aug 25, 2007

megaforcetkd

OH so...

Vavg = (2x)/((x)/(80kph)) + ((x)/60kph)).

11. Aug 25, 2007

learningphysics

Yup. That's right. You can simplify.

12. Aug 25, 2007

megaforcetkd

AHHHH! Ok thanks :D. I guess I just wasn't thinking =/ We did this first day of AP Physics.

13. Aug 25, 2007

learningphysics

What did you get as the final answer?

14. Aug 25, 2007

megaforcetkd

68.57 km/h

15. Aug 25, 2007