Problema Solution
James has to cycle the four miles to university each day. He starts out on monday, but his bike gets a puncture partway (x miles alomg the route) and he has to push it the rest of the way. His walking speed, w, when pushing his bike is 1/3 of his cycling speed. On tuesday , he only gets half as far before geting a puncture and it takes him 1 1/2 times as long to reach the university as it did on monday. On wednesday he doesnt get a puncture at all. What fraction of mondays time, t, does he take to get there on wednesday
Answer provided by our tutors
Let
v = the cycling speed
(1/3)v = the walking speed
d = the distance to university
The time James spent on Monday is:
x/v + (d - v)/((1/3)v) = (1/v)(x + 3d - 3v)
The time James spent on Tuesday is:
(d/2)/v + (d/2)/(v/3) = (1 1/2)*(1/v)(x + 3d - 3v)
2d/v = (3/2)(1/v)(x + 3d - 3v) divide both sides by 2
d/v = (3/4)(1/v)(x + 3d - 3v)
The time James spent on Wednesday is d/v but we know that:
d/v = (3/4)(1/v)(x + 3d - 3v)
d/v is 3/4 of the Monday time.