Trip from San Antonio to Houston

[rudransh verma]

Homework Statement

You drive on Interstate 10 from San Antonio to Houston, half the time at 55 km/h and the other half at 90 km/h. On the way back you travel half the distance at 55 km/h and the other half at 90 km/h. What is your average speed (a) from San Antonio to Houston, (b) from Houston back to San Antonio, and (c) for the entire trip? (d) What is your average velocity for the entire trip?

Relevant Equations

Average speed=total distance/total time
Average velocity=total displacement/total time

How do you approach the problem as if you have never done it before?

 

[hmmm27]

How do I approach the problem as if I have never done it before?

Have you done it before ?

If not, I imagine first you'd try to make sure you understand the parameters of the exercise ; then, try to understand the solutions required.

If so, then maybe try using a different method to solve.

 

[berkeman]

Homework Statement:: You drive on Interstate 10 from San Antonio to Houston, half the time at 55 km/h and the other half at 90 km/h. On the way back you travel half the distance at 55 km/h and the other half at 90 km/h. What is your average speed (a) from San Antonio to Houston, (b) from Houston back to San Antonio, and (c) for the entire trip? (d) What is your average velocity for the entire trip?
Relevant Equations:: Average speed=total distance/total time
Average velocity=total displacement/total time

How do you approach the problem as if you have never done it before?

It's good to start by defining some names for the various quantities involved. Then write the equations that relate the quantities to the word problem descriptions, and try to solve the multiple equations. Usually you will have the same number of equations as the number of unknowns, so you should be able to solve the problem numerically and get a single answer for each of the questions.

So I would start by calling the two locations "A" for San Antonio and "H" for Houston, and define the time for the first part of the trip as $t_{AH}$. The time for the return trip is $t_{HA}$. On the trip back you drive the distance $\frac{d_{HA}}{2}$ at the first speed, and $\frac{d_{HA}}{2}$ at the second speed.

Use that kind of naming convention for the various distances, times and speeds ionvolved in the problem, and then write the equations that calculate the unknown average speeds, etc. Substitute the numbers that you know (like the speeds you are given), and see if you can solve the equations to get the answers for the different parts of the question.

Give that a try and see where you end up. You can use LaTeX like I did to post your work here in the forum window -- see the LaTeX Guide link below the Edit window, or just click "Reply" on my post to see how I wrote the LaTeX equations. If you post the equations in-line, you use a double-# delimiter before and after each equation, and if you want the equation on its own line, you use a double-$ delimiter.

 

[Frabjous]

This is an irresponsible problem. I grew up in Texas. You might get shot for driving in km/hr and you will get shot for driving 34mph when the speed limit is at least 55mph.