Question 423820: Please help me solve this word problem: It takes a freight train 2 hours more to travel 300 miles than it takes an express train to travel 280 miles. the rate of the express train is 20 miles per hour faster than the rate of the freight train. Find the rates of both trains.
I have been working on this problem for 3 days.
Answer by sudhanshu_kmr(1152)   (Show Source):
You can put this solution on YOUR website! 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
if any doubt, please contact....
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