What Time Did David Reach Point A After Passing Carl?

[Quark Itself]

Problem : Two hikers, Call them Carl and David started to walk at 12pm (noon) along the same path but in opposite directions. Let's assume Carl walked from Point A to point B and David did the opposite, walked from Point B to Point A. Both of them have different constant speed. They pass each other at a point at 1500 hours. Carl arrived at Point B , 2.5 hours before David arrived at point A. When did David arrive at point A?

Attempt: Carl Case 1) Xf = Xi + ViT assuming that his initial point Xi = 0 makes David's Xf = 0 as well.
Xf = 0 + 3Vi. this Xf is the meeting point, therefore they have been walking for 3 hours, hence the 3Vi.
Then I got stuck..

Thanks in advance !

 

[daveb]

Since they meet at 3:00, their elapsed times are equal, though the distance traveled are different. When the walk is over their distances are equal though the elapsed times are different.

 

[Quark Itself]

Yeah, I got that part and everything. It is very clear, but from there how do you proceed?

 

[Ray Vickson]

Yeah, I got that part and everything. It is very clear, but from there how do you proceed?

Set it up carefully and explicitly. For example, let A be at x = 0 and B be at x = L. Let Carl's speed be c and David's speed be d. Then Carl's position xc(t) is xc(t) = c*t for t <= L/c and David's position is xd(t) = L-d*t for t <= L/d. Now you have xc(3)=xd(3), and you have one other relationship regarding the endpoints. If you write things properly you will see that you do (believe it or not) have enough information to complete the question.

RGV

 

[rwisz]

Based on the given information, we can set up the following equations:

1. Carl's journey: Xf = Xi + ViT
2. David's journey: Xf = Xi - ViT

Where:
- Xf = final distance
- Xi = initial distance (in this case, 0 as both hikers started at opposite points)
- Vi = constant speed of each hiker
- T = time taken for both hikers to reach the meeting point

Since they both reach the same meeting point at the same time, we can set the two equations equal to each other:

Xi + ViT = Xi - ViT

We also know that Carl arrived at Point B 2.5 hours before David arrived at Point A, which means that T = 2.5 hours for David's journey.

Substituting this value into the equation, we get:

Xi + Vi(2.5) = Xi - Vi(2.5)

2Xi = 5Vi

Solving for Xi, we get: Xi = 2.5Vi

This means that David's initial distance is 2.5 times Carl's initial distance. Since they are walking in opposite directions, David's final distance (Point A) will also be 2.5 times Carl's final distance (Point B).

We also know that they both reached the meeting point after 3 hours of walking, so we can set up another equation:

Carl's journey: Xf = 3Vi
David's journey: Xf = 2.5(3Vi) = 7.5Vi

Since they both reach the same meeting point, we can set these two equations equal to each other:

3Vi = 7.5Vi

Solving for Vi, we get: Vi = 0.4

This means that Carl's constant speed is 0.4 units per hour and David's constant speed is also 0.4 units per hour.

Now, to find out when David arrived at Point A, we can use the equation Xf = Xi - ViT and substitute the values we have calculated:

Xf = 2.5(0.4) - 0.4(T)
0 = 1 - 0.4T
0.4T = 1
T = 2.5 hours

Therefore, David arrived at Point A at 1500 hours + 2.5 hours =