Question 320518: Two trains leave the same city at the same time, one going north and the other east. The northbound train travels 20 mph faster than the east bound one. If they are 300 miles apart after 5 hours, what is the speed of each train?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Two trains leave the same city at the same time, one going north and the other east. The northbound train travels 20 mph faster than the east bound one. If they are 300 miles apart after 5 hours, what is the speed of each train?
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east bound train speed be xmph
north bound train = x+20 mph
east bound train after 5 hours - distance = 5x
north bound train after 5 hours - distance = 5(x+20)=5x+100
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The distance is a hypotenuse of a right triangle with 5x & 5(x+20) as the legs
(5x)^2 +[5x+100]^2= 300^2
25x^2+[25x^2+1000x+10000]= 90000
25x^2+25x^2+1000x+10000=90000
50x^2+1000x-80000=0 ( divide by 50)
x^2+20x-1600=0
Find the roots of the equation x1 x2
x1= (-20+sqrt(20^2+6400)/2)
x1= 31.23 speed of east bound train
x2=(-20-sqrt(20^2+6400)/2)
x2=-51.23 ( ignor negative value
speed of north bound train = 51.23 mph
CHECK
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