Bill leaves his house for Makayla's house riding his bicylce at 8mph. At the same time, Makayla leaves her house heading toward Bill's house walking at 3mph. Write a system of equations to represent the distance, d, each is from Makayla's house in h hours. They live 8.25 miles apart. Solve the system to determine how long they travel before meeting.

Question

anonymous · Answer

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This is a Kinematics problem. So we know the velocity of Bill and Makayla and the distance between their two houses.

let "d" represent the distance from the reference point of Makayla's house as stated in the opening question, and "h" as the time. So if we were to put this into a function of the amount of distance(d) from Makayla's house in respect to time(h):

$$d _{bill}(h) = x - v _{bill}h$$$$d _{Mak}(h) = v _{mak}h$$

To find the time when they reach each other, we know that they will be at the same distance away from Makayla's house in which the $$d _{bill}  = d _{Mak}$$

If that is true, we set the equations equal to each other and then solve for "h".