# math

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I need help to get started with writing the equation for the following problem: It takes a freight train 2 hours longer 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 greater than the rate of the frieght train. Find the times and rates of both trains

• math -

let the speed of freigh train be x mph
then speed of express is x+20 mph

time for freight to go 300 miles = 300/x
time for express to go 280 = 280/(x+20)

300/x - 280/(x+2) = 2
multiply by x(x+20)
300(x+20) - 280x = 2x(x+20)
300x + 6000 - 280x = 2x^2 + 40x
2x^2 + 20x - 6000 = 0
x^2 + 10x - 3000 = 0
(x+60)(x-50) = 0
since x > 0, x = 50

speed of freight = 50 mph
time for freight to go 300 miles = 6 hours

speed of express = 70 mph
time to go 280 miles = 4 hours

(sure enough the difference between their times is 2 hours.)

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