Brandon starts running from the starting line of a track at a speed of 10 ft. per second. 60 seconds later david starts from the same point and runs in the same direction at a speed of 12 per second Let y represent brandons time and let x represent davids time. Write a system of equations that can be used to find how long it will take david to overtake brandon?

Question

Brandon starts running from the starting line of a track at a speed of 10 ft. per second. 60 seconds later david starts from the same point and runs in the same direction at a speed of 12 per second Let y represent brandons time and let x represent davids time. Write a system of equations that can be used to find how long it will take david to overtake brandon?

Answer 1

y = x+10

when david overtakes brandon, their distances are equal.
Distance = speed * time
so,

10y = 12x
so,
10(x+10) = 12x
100 = 2x
x = 50
y = 60

So, Brandon ran 60sec*10ft/sec = 600 ft
David ran 50sec * 12ft/sec = 600 feet

So, the question is, how long did it take David to overtake Brandon?