Strategies for Solving Uniform Motion Problems

[Amano]

Homework Statement

The member of a girls club hiked to lake tenkiller at 2 mph. Then they got a ride back home at 12 mph. Find their hiking time if it was 5 hours longer than their riding time. How far was it to the lake?

Now I know this is a simple question. Very easy. But the reason I write this one out is not for help. But I want better knowledge on better was to do this question.


2.Relevant equations

Can't add anything here I don't think.

The Attempt at a Solution

I just want to know how many ways I can do this question. I know there is one with graphs that you can do to answer this question. Are there others?

The way I have been taught to do this question by my textbook is this way.


Dh Dh=Dr RhTh= RrTr
-------->
Dr
<------- Rh=2 Rr=12 Th=Tr+5

2[Tr+5]= 12Tr

2Tr+10 = 12Tr
10 = 10Tr
Tr = 1


Th= Tr+5
Th= 6hr

Thus the distance will = 12 miles when 6 is multiplied by the 2.

Now that is the way I have been doing it. My only trouble is that I dont' see there is any reason to do so much algebra. so when I skimp of some of the writing like this.

2T+10 = 12T And I find this work quite well. But I find that you can get easily confused at times depending on what is going on, with the question and it's wording.

So what would some of you guys do?

Cheers,
Amano

p.s sorry if I post this in the wrong place.

 

[Redbelly98]

Welcome to PF

These problems can also be done by making a table:

                  Distance     Avg speed     Time
Up Mountain                        2          t+5
Ride home                         12          t
Total trip     ***not relevant***

Then you can use the relation

Distance = Speed × Time​

and go from there.

You get the same algebraic equation, but often the table helps to organize things better. Especially in problems where the combined total trip comes into play, though it didn't this time.

 

[Amano]

Hi,
Thanks for the reply. It looks much better than the [to me clumsy.] way I was setting them out.

Cheers for your help.

Amano