# Algebraic rate problem

## Homework Statement

Andy is 100 feet from Bob and Bob is 300 feet from Charlie and they are all facing the same direction on the same line.
They all begin to move in the same direction that they are facing at relative constant speeds.
In 6 minutes, Andy reaches Bob, and in another 6 minutes, Andy reaches Charlie.
How many minutes will it take for Bob to reach Charlie?

d = r * t

## The Attempt at a Solution

So I've drawn the initial problem like this:

Code:
A ---------- B ------------------------------ C
100                    300

So A -> C = 400.

In 6 minutes, all A, B, and C will have moved a certain distance, so Andy's distance traveled = Bob's distance traveled + 100:

(R_A = Rate of Andy, R_B = Rate of Bob):

(R_A)(6) = 100 + (R_B)(6)

But Charlie has also traveled another 6 minutes worth of distance so I have to keep that in mind.

So in another 6 minutes, Since Andy was in the same position as Bob but is now up to Charlie (Charlie has traveled 12 minutes now also):

(R_A)(6+6) = (R_C)(12) + 400

I think. I'm not even sure if this is the correct distance traveled so far.

How do I find how far Bob traveled in 12 minutes?

(R_B)(12) = ???

Last edited:

HallsofIvy
Homework Helper

## Homework Statement

Andy is 100 feet from Bill and Bill is 300 feet from Charlie and they are all facing the same direction on the same line.
They all begin to move in the same direction that they are facing at relative constant speeds.
In 6 minutes, Andy reaches Bill, and in another 6 minutes, Andy reaches Chelsea.
How many minutes will it take for Bill to reach Chelsea?
What happened to Charlie?

d = r * t

## The Attempt at a Solution

So I've drawn the initial problem like this:

Code:
A ---------- B ------------------------------ C
100                    300

So A -> C = 400.

In 6 minutes, all A, B, and C will have moved a certain distance, so Andy's distance traveled = Bob's distance traveled + 100:
And now Bill has changed to Bob?

(R_A = Rate of Andy, R_B = Rate of Bob):

(R_A)(6) = 100 + (R_B)(6)
So you have R_A= (6R_B+ 100)/6

[quogter]But Charlie has also traveled another 6 minutes worth of distance so I have to keep that in mind.

So in another 6 minutes, Since Andy was in the same position as Bob
I have noi idea what you mean by that.
but is now up to Charlie (Charlie has traveled 12 minutes now also):

(R_A)(6+6) = (R_C)(12) + 400
Good. And so R_C= (12R_A- 400)/12. Now replace R_A with (6R_B+100)/6 to get a relation between R_C and R_B.

I think. I'm not even sure if this is the correct distance traveled so far.

How do I find how far Bill traveled in 12 minutes?

(R_B)(12) = ???
Frankly, the switch from "Charlie" to "Chelsea" and back again and the change from "Bill" to "Bob" makes me wonder how much attention you gave to this problem.

Sorry, I fixed the problem. I have been working on it since yesterday and I still don't understand any of it, even when looking at the solution so I'm a little frustrated.

The solution process says that:

(12)R_A = (12)R_C + 400

So in 12 minutes when Andy reaches Charlie, doesn't Andy need to cross: 100 ft + Bob's covered distance + 400 ft. + Charlie's covered distance? How come Bob's distance is omitted entirely? It seems like Andy just skipped over Bob and only covers the distance to reach Charlie, since Charlie didn't travel the distance Bob did at all, so Andy has to travel that first to cover Charlie's distance as well.