RTD Comparing a CAT to a OG question

[AbigailS228]

Question from CAT 4 states: At 10:00 a.m., Peter begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 2:00 p.m., John begins traveling from Riverdale on the same path at a constant rate of 15 mph, at what time will he catch up to Peter?

Question from OG13 #207 states: [deleted because problem is from a banned source - see below]

So I get confused when making my RTD chart when I add the extra distance/hours...this is what the book says to do:
Peter John A B
r 10 15 r 58 50
t t (+4) t t t t
d d d d d(+20) d **later add 8

BUT I want to change the Peter and John equation to Peter=t and John=t+4
The reason I'm confused is because Car A is behind Car B by 20 miles (and I'm supposed to add to Car A's distance), but John is behind Peter by 4 hours (so why do I ADD to Peter and not John?)

[pierNYU]

Hi AbigailS228,
I tackled the first question differently, without setting up equations.

I literally draw the following:

10 11 12 13 14 15 16 17 18 19 20 21 22

P 0 10 20 30 40 50 60 70 80 90 100 110 120
J 0 0 0 0 0 15 30 45 60 75 90 105 120

So you know that J will catch peter at 22.00

For the second question I think you are missing a part?
Once I get back home I will have a look at the question!

/Pier

[AbigailS228]

I apologize, the formatting did not come out right so my question did not make as much sense as I intended.

I get tripped up when someone is behind 20 miles or 4 minutes... In the first example Peter began first, but John is 4 hours behind, so how do I know who to add the 4 hours on to (I like the equation way better-sorry!)
-I am supposed to add 4 to Peter (who's in front)
In the second example
Car A is behind 20 miles
-I am supposed to add 4 to Car A (who's behind)

Aren't I doing the opposite in the two questions?

[tim]

OG is a banned source; it is illegal to post OG questions anywhere on the web. If you are in one of our classes, please ask OG questions during office hours or before/after class.

As for the problem you reference, you are not reading the explanation correctly. I have looked the problem up in our database, and what you have written does not correspond to the explanation as you claim. Please look up the explanation again and let us know if you have any further questions.

[AbigailS228]

I apologize about that.

This is the explanation given:

"Let's use the Rate/Time/Distance chart below to organize the information in this problem. Since John left four hours later than Peter, his time can be represented as t – 4.

When Peter and John meet, their distances will be equal: 10t = 15(t – 4) or t = 12. If Peter will have been cycling 12 hours when they meet, they will meet at 10:00 p.m. The correct answer is E."

So in other words, John's time labeled at t-4 is the same as adding 4 to Peter's time (from my understanding of rate and work problems).

Now John is behind Peter by 4 hours, so why wouldn't I add 4 to John (or subtract 4 from Peter)? The reason I originally referenced the other question is because it appears you're supposed to do the opposite when a certain vehicle is 20 miles behind (add to 20 that vehicle or subtract 20 from the other vehicle). Is this because distances and times are not treated the same way?

[RonPurewal]

Apples and oranges. Being literally "behind" someone, in terms of distance, can't be meaningfully compared to being (figuratively) "behind" someone in terms of time.

If you are trying to figure out where the "+" and "-" signs go, just think about the corresponding basic concepts of "more" and "less".

If there's a 4-hour difference, just ask yourself: Who spends more time? Who spends less time?

If there's a difference of 20 miles, just ask yourself: Who travels more miles? Etc.

If you just think literally enough about what the "+" and "–" signs mean, the issue should take care of itself.

[AbigailS228]

Ron-

So I thought I understood what you're saying until I came across this in CAT6..

Pascal has 96 miles remaining to complete his cycling trip. If he reduced his current speed by 4 miles per hour, the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50%. What is his current speed?

6
8
10
12
16

I got the equations right up until I had to add the 16. So this is the correct equation:
96/(r-4) = 96/1.5r + 16

I put the +16 on the other side, because when he reduced his speed 4 mph it would take him 16 minutes longer so I had..
96/(r-4) +16 = 96/1.5r

I'm sorry I keep asking this question again and again but it is repeatedly the only part of RTD questions I am getting wrong so I'm trying really hard to wrap my mind around what I don't get logically.

[tim]

So this 96/(r-4) and 96/1.5r - what are they measuring? And which one is bigger? That will help you figure out where to put the 16 to make them equal.