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Candice leaves on a trip driving at 25 miles per hour. Four hours later, her sister Liz starts from the same location driving at 50 miles per hour. How long after Liz leaves home will she catch up to Candice?

 Aug 29, 2020
 #1
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Let Candice's time when Liz catches up with her =T

Liz's time when she catches up with Candice        =T - 4

 

25T =50(T - 4), solve for T

 

T = 8 hours from the time Candice left, or:

8 - 4 = 4 hours from the time Liz left.

 Aug 29, 2020
 #2
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Candice leaves on a trip driving at 25 miles per hour. Four hours later, her sister Liz starts from the same location driving at 50 miles per hour. How long after Liz leaves home will she catch up to Candice?   

 

When Liz leaves, Candice is 100 miles away. 

 

Liz, going 50, takes 2 hours to get to that spot. 

But by then, Candice is another 50 miles away. 

 

So Liz, going 50, takes 1 hour to get to the next spot. 

But when she gets there, Candice has moved 25 miles farther. 

 

Liz presses on, at 50, and gets to the new spot in a half hour. 

In that half hour however, Candice has moved on another 12.5 miles. 

 

Liz can keep cutting the distance in half, but can never catch Candice. 

 

Obviously this isn't true; Liz can catch Candice. 

But can you explain what's wrong with the logic? 

.

 Aug 29, 2020
 #3
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Actually, yes, there is something flawed with that logic.

 

Let's take a step back:

 

Instead of comparing them two, we can just pretend there is a guy that keeps on walking half his distance to get to his house. Let's pretend that he is one mile away from his house. So, here is how much space is left from him to his house:

 

1/2, 1/4, 1/8, 1/16, 1/32

 

Sure, it's going to take him forever (literally forever, not just hyperbolicly), BUT, he WILL get there. That's just some number sense and calculus combined.

 

Now, I will describe you what is wrong with your logic.

 

Sure, the begining is right: Candice WILL be 100 miles away. Let's just run down the line: (the first is candice, and the second is liz)

 

After 4 hours: 100 : 0   

After 5 hours: 125 : 50

After 6 hours: 150 : 100

After 7 hours: 175 : 150

After 8 hours: 200 : 200

 

See? We have already landed on the same spot.

 

What you are thinking is that Liz keeps on cutting the distance in half, but nowhere in the problem did it say that. Just because there is a pattern in the begining, does not mean it will last. Sometimes, me included, mathmeticians get sidetracked based on false, groundless (not only groundless, but already proved wrong) ideas. 

 

We have now also gotten the answer: hours

 

This can also be done algebraicly:

 

Let "h" be the amount of hours driven. 
 

100 + 25 h = 50 h

100 = 25h

h = 4

 

MISTAKE CORRECTED THANKS TO ABOVE GUEST! Congratulations 🎊🎉🎈🍾 

 

:)

ilorty  Aug 29, 2020
edited by ilorty  Aug 29, 2020
edited by ilorty  Aug 29, 2020
 #4
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Hello ilorty.  That's a very good analysis.  One slip: "After 4 hours: 100 : 50"   Actually, after 4 hours Liz is starting at 0.  But that isn't important.  I figured you would know the flaw in the "half distance" reasoning; I was trying to prompt the OP (original poster) to think about it. 

.

Guest Aug 29, 2020
 #5
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+1

Ahhh. Yes! Let me correct my mistake, and also I will give you some credit!

ilorty  Aug 29, 2020

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