SOLUTION: In the Canada, Medicine Hat and Cranbrook are 300 km apart. Sam rides his motorcycle 20 km per hr faster that Brian rides his motorcycle. Find Sam's average speed if he travels fro

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Question 384299: In the Canada, Medicine Hat and Cranbrook are 300 km apart. Sam rides his motorcycle 20 km per hr faster that Brian rides his motorcycle. Find Sam's average speed if he travels from Cranbrook to Medicine Hat in one and one quarter of an hour less time than Brian.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
In the Canada, Medicine Hat and Cranbrook are 300 km apart. Sam rides his motorcycle 20 km per hr faster that Brian rides his motorcycle. Find Sam's average speed if he travels from Cranbrook to Medicine Hat in one and one quarter of an hour less time than Brian.
...
Brian's speed = x mph
Brian's time = 300/x
..
Sam's speed = x+20
sam's time = 300/(x+20)
..
Time Brian - Time Sam = 1 1/4 = 5/4
..
300/x -300/(x+20)= 5/4
..
LCD + x(x+20)
%28-300%2Ax%2B300%2A%28x%2B20%29%29%2Fx%28x%2B20%29=5%2F4
...
%28300x-300x%2B6000%29%2Fx%28x%2B20%29=5%2F4
..
%286000%29%2F%28x%28x%2B20%29%29=5%2F4
cross multiply
5x(x+20)=4*6000
5x^2+100x=24,000
-24,000 -24,0000
5x^2+100x-24,000=0
/5
x^2+20x-4800=0
x^2+80x-60x-4800=0
x(x+80)-60(x+80)=0
(x+80)(x-60)=0
%28highlight%28x=60+mph%29%29 Brian's speed
%28highlight%2880+mph%29%29 Sam's speed
....
m.ananth@hotmail.ca