Subject: need help
Name: carmen
Who are you: Other

hi, i need help solving the following problem. i don't understand how to do it. and there's several problems like this that will be coming up on one of my exams. if you can, can you please explain step by step how you would solve or go about solving this problem.

problem: cary was going to meet jane at the airport, if he traveled 60mph, he would arrive one hour early, and he traveled 30 mph, he would arrive one hour late. how far was the airport? recall: distance=speed(time)

Hi Carmen.

You can find the solution if you identify

1. What you are trying to find
   
   
2. What you know
   
   
3. How the different quantities are related to each other.

Let's do that with your question:

1. You want to find the distance, so let's call it D.
   
   
2. You know that if Cary goes 60 mph, he gets there 1 hour early AND if he goes 30 mph, he gets there 1 hour late. So if he goes 30 mph, he gets there 2 hours later than if he goes 60 mph.
   
   
3. Distance = speed x time. Let's write this as D = ST where T will be the time it takes him to get there if he goes 60 mph.

Now you fill in the relationship(s) in part 3 with the values in part 2:

D = 60T

and

D = 30(T+2)

Because he goes the same distance D, but the time is 2 hours more than the time for the faster speed.

So now you have two equations with two unknown values - only one of which you really care about. To solve this, you need to eliminate the other variable (T). There are several ways of doing this, but I often find the easiest way is to solve both equations for the variable you don't care about first:

D = 60T therefore T = D/60,

and

D = 30(T+2) therefore D = 30T + 60

therefore

T = D/30 - 2

Now remember that when two things equal a third thing, then the first two things have to equal each other, so

T = D/60 and T = D/30 - 2

means

D/60 = D/30 - 2

and the rest I'll leave to you.

Hope this explanation helps,
Stephen La Rocque.