How Fast Did Alex and Jessica Travel in Opposite Directions?

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Discussion Overview

The discussion revolves around a mathematical problem involving two individuals, Alex and Jessica, who travel in opposite directions from a common starting point. The problem requires determining their speeds based on the distance between them after a certain time. The scope includes mathematical reasoning and problem-solving strategies related to distance, speed, and time.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant initially calculated the distances traveled by Alex and Jessica incorrectly, leading to an erroneous conclusion about their separation distance.
  • Another participant pointed out that the distances were miscalculated due to the assumption that both traveled in the same direction, rather than opposite directions.
  • A later reply suggested using algebra to define the speeds of Alex and Jessica, proposing equations based on their relationship and the total distance apart.
  • One participant emphasized the importance of using a simpler method and provided a structured approach to set up the equations.
  • Another participant presented a tabular method to clarify the relationship between speed, time, and distance, leading to a calculated solution for their speeds.

Areas of Agreement / Disagreement

Participants generally agree on the need to correct the initial misunderstanding regarding the direction of travel. However, there are multiple approaches suggested for solving the problem, and no consensus on a single method is reached.

Contextual Notes

Some participants noted the importance of using algebraic methods and provided different strategies for approaching the problem. There are unresolved assumptions regarding the setup of the equations and the interpretation of the problem.

Who May Find This Useful

This discussion may be useful for students seeking assistance with similar distance, speed, and time problems, particularly in a homework context.

Richay
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At exactly 5 p.m., Alex rode off from Asteroid. One hour later, Jessica rode off from Asteroid in the opposite direction at a speed 400 kph less than that of Alex. If they were 7900 km apart at 11 p.m., how fast did each travel?

Answer in the form: Alex, Jessica

Okay, my teacher says i got this problem WRONG but he won't help me figure it out.

This is what i did.

------------------------------------------

Answer: 5900, 5500

5,900 X 6(5 pm to 11pm is 6 hours = 35,400
5,500 x 5(6pm to 11pm is 5 hours) = 27,500

35,400 - 27,500 = 7,900

--------------------------------------------


What am i suppose to do instead?





And if anyone has any extra time. How do i solve this one?

Prince Henry and Princess Clay were 63 miles apart at dawn. Prince henry began the journey to the meeting place at 7 a.m. at 3 mph. Three hours later, Princess Clay went out to meet him. If they met at 4 p.m., how fast did each travel?

(I'm mostly curious about the first one :rolleyes: )
 
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Although this isn't the place for homework help, I'll give it a try anyways.:smile:

Basically, the problem I see with how you worked your first problem is that your velocities (and distances traveled) are WAY too large. Just think about it. If Alex traveled 35,400 km to the right, and Jessica traveled 27,500 km to the left, then the distance apart is not 7,900 km. According to your answer they are 62,900 km apart. With that in mind try working it again.
 
Damn. I think i know what i did wrong then. They were going in opposite directions, not in the same direction. That's where i screwed up i believe.

Oh, and I'm not here for the answers really. I need to know how to solve the math problems i don't understand how to do. =]
 
By the wrong place I meant the wrong "place" within the forum. There is a section dedicated to homework help.

When you get the problem worked out (if you do it soon) then re-post your answers and we can compare. But I think you understand it now anyways.
 
Richay said:
Damn. I think i know what i did wrong then. They were going in opposite directions, not in the same direction. That's where i screwed up i believe.

Oh, and I'm not here for the answers really. I need to know how to solve the math problems i don't understand how to do. =]
Yes, we assume that- and those problems should be posted in the homework help section.
 
Greetings, Richay.

I am probably a year late on this as I did not check the date, but am reviewing for my ACT. When I took a look at this problem, the first thing I noticed you did wrong was not use the simplest method.

Just use algebra. A lot of schools don't teach you how to apply it to daily life, and here's more or less a chance of doing so.

Define Alex as X.

Define Jessica as X - 400. Why? Because she ends up being 400 less than Alex (X) .

If our ending total is 7900, what must be done?

x + ( x - 400 ) = 7900

That's pretty much a given at this point. You said you don't want answers, but if you're asking for help, that was needed to at least get you in the right direction and how to assess a problem like this in the future.

Figure out the answer on your own, but double check unless you're on a test that's timed.

X = Set Value

X - 400 = Set Value

Does 2X - 400 = 7900?

Yes, it does. Now it's up to you to figure out what the X's stand for, which I'm sure you'll have no problem doing.
 
Oh, and I forgot to add you must divide the answers by 6.

D = vt

T in this case is equal to 6.
 
Let x=rate of Alex
x-400=rate of Jessica

Person r t d
Alex x 6 6x
Jessica x-400 5 5x-2000
NOTE: ASSUME THIS IS IN TABULAR FORM.
6x+5x-2000=7900
6x+5x=7900+2000
11x/11=9900/11
x=900
x-400=500

Therefore, the rate of Alex is 900kph while the rate of Jessica is 500kph.
 

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