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. 
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Brian's speed = x mph
Brian's time = 300/x
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Sam's speed = x+20
sam's time = 300/(x+20)
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Time Brian - Time Sam = 1 1/4 = 5/4
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300/x -300/(x+20)= 5/4
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LCD + x(x+20)
{{{(-300*x+300*(x+20))/x(x+20)=5/4}}}

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{{{(300x-300x+6000)/x(x+20)=5/4}}}
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{{{(6000)/(x(x+20))=5/4}}}
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
{{{(highlight(x=60 mph))}}} Brian's speed
{{{(highlight(80 mph))}}} Sam's speed

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m.ananth@hotmail.ca