When Will John Catch Up to Mary?

[Larrytsai]

Mary left home at noon running at 7m/s towards school. Her brother John left 35 seconds later running at 8m/s. How much time passed and how far were they from the house when John caught up to Mary.

Homework Equations

My solution i tried was to the x-y graph. My notes saids I am supposed to use these formulas
d-d0=vt , d=vt

The Attempt at a Solution

I tried graphing as an university friend/student has told me but it just doesn't work out because when I get to john i have no clue to where i start on the graph to graph johns distance. All i know right now is that in 35 seconds, when john leaves Mary is at 245 metres.

 

[bob1182006]

ok those equations are correct the thing is you need to have 2 equations for the distance.
One will represent Mary, another will represent John.

$$d_{Mary}=d_0+vt$$
$$d_{John}=d_0+vt$$

since velocity is constant a=0 and we loose that a/2*t^2 part.

So when should time start for these equations?
t=0 Mary leaves the house? or
t=0 John leaves the house, Mary has a 35s lead and is how many m away from the house already?

 

[m2003]

As a scientist, your approach to solving this problem would involve using the equations of motion to determine the time and distance at which John catches up to Mary. The first step would be to define your variables: d0 is the initial distance (in this case, the distance from the house), d is the final distance (also the distance from the house), v is the velocity, and t is the time.

Using the equation d = vt, we can determine the distance that Mary has traveled in t seconds, which is 7t meters. Similarly, John has traveled a distance of 8(t-35) meters in t seconds, since he left 35 seconds later.

Since we know that John catches up to Mary at some point, we can set their distances equal to each other and solve for t:

7t = 8(t-35)
7t = 8t - 280
t = 280 seconds

So, after 280 seconds, John has caught up to Mary. To find the distance from the house at this time, we can plug t = 280 into either equation:

d = vt = (7)(280) = 1960 meters

Therefore, after 280 seconds, John has caught up to Mary and they are 1960 meters from the house.