Problema Solution
George and Bill left town A for town B at the same time. George was riding a bicycle at a constant speed, while Bill was driving a car. Bill traveled 5 times faster than George. Bill's car broke halfway, and the rest of the way to the town B Bill traveled by foot with a speed equal to half of George's bicycle speed. Who got to B first?
Answer provided by our tutors
let
x = the speed of George riding a bicycle
t = the time of George
d = the distance from A to B
speed = distance / time => time = distance/speed
Bill traveled by car 5 times faster than George that is with a speed: 5*x
Bill traveled by food with speed equal to half of George's bicycle speed: x/2
the time that George needs to arrive from A to B is: t = d/x
the time that Bill needs to arrive from A to B is = the time traveled by car (halfway) + the time traveled by foot
(d/2)/(5*x) + (d/2)/(x/2) = (d/x)(1/10 + 1) = (d/x) * (11/10)
lets compare the two times:
(d/x) * (11/10) > d/x
the time of Bills trip > the time of Georges trip
this means that George got to town B first.