Two people, Paige and Sandy, are racing each other. Assume that both their accelerations are constant, Paige covers the last 1/8 of the race in 5 seconds, and Sandy covers the last 1/5 of the race in 8 seconds. Who wins, and by how much?

Answer 1

let Page's acceleration be a
let Sandy's acceleration be b

Page's velocity is at + c
Sandy's velocity is bt + k
at t=0, both their velocities should have been zero, so c = 0, k=0

then if the distance of the race is x units
then for Page: 5a = x/8 ---> x = 40a
for Sandy : 8b = x/5 ---> x = 40b
40a = 40b
a = b
they have the same velocity.

It is a tie ?

Am I missing something here?

Answer 2

You forgot to include velocity. Using the equation distance= 1/2at^2+vt, one can plug in t (time) and distance.