Question 423820
speed of freight train = x mph

speed of express train = x+20  mph

time taken by freight train for 300 miles = 300/x  hrs

time taken by express train for 280 miles = 280/(x+20) hrs


300/x  = 280/(x+20)   + 2

=> 300/x - 280/(x+20) =  2


=> [ 300(x+20) -280x]/x(x+20) = 2


=>[ 20x + 6000] = 2(x^2 +20x)


=> 20x + 6000 = 2x^2 + 40x

=> 2x^2 + 20x - 6000 = 0

=> x^2 + 10x - 3000 = 0

=> x^2 + 60x - 50x - 3000 = 0

=> x(x+60) -50(x +60)=0

=>(x-50)(x+60) = 0

now, x=50 mph because, x= -60 not possible.

so, speed of freight train = 50 mph

speed of express train = 70 mph




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