SOLUTION: 1. A passenger train leaves a train depot two hours after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rat

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Question 174307: 1. A passenger train leaves a train depot two hours after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of the passenger train if the passenger train overtakes the freight train after 3.2h.
2. Find the slope and y-intercept of the line -2x+3y=3.
3. find the equation of the line that contains the point (-1,0)and has a slope of 2.
Answer by stanbon(75887) (Show Source):
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1. A passenger train leaves a train depot two hours after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of the passenger train if the passenger train overtakes the freight train after 3.2h.
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Passenger train DATA:
time = 3.2 hours ; rate = x mph; distance = rt = 3.2x miles
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Freight train DATA:
time = 5.2 hours ; rate = (x-20) mph ; distance = rt = 5.2(x-20) miles
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Equation:
distance = distance
3.2x = 5.2(x-20)
3.2. = 5.2x - 104
2x = 104
x = 52 mph (rate of the passenger train)
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2. Find the slope and y-intercept of the line -2x+3y=3.
y = (2/3)x + 1
slope = 2/3
intercept = 1
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3. find the equation of the line that contains the point (-1,0)and has a slope of 2.
Form: y = mx+b
intercept: 0 = 2*-1 + b
b = 2
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Equation :
y = 2x + 2
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Cheers,
Stan H.