The First car covers a distance of 400 km at a certain speed and second car covers a same distance less than one hour of the first car if first car speed was less than 20km of second car and what is the first car speed
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Let the speed of second car = x km/h
then the speed of first car = x -20 km/h
Time taken by the 1st car to travel 400 km = 400/x-20 h [time = distance/speed]
Time taken by the 2nd car to travel 400 km = 400/x h
According to the sum
400/x-20 - 400/x = 1 hour
(400x + 8000 - 400x)/x² - 20x = 1
8000 = x² - 20x
x² - 20x - 8000 = 0
x² - 40x + 20x - 8000 = 0
x(x-40) + 20(x-40) = 0
(x-40) (x+20) = 0
x = 40 or -20
So x = 40 km/h [speed is not in negative. So, we do not x = -20]
Therefore the speed of the first car = 20 km/h[x-20 = 40-20=20km/h]
then the speed of first car = x -20 km/h
Time taken by the 1st car to travel 400 km = 400/x-20 h [time = distance/speed]
Time taken by the 2nd car to travel 400 km = 400/x h
According to the sum
400/x-20 - 400/x = 1 hour
(400x + 8000 - 400x)/x² - 20x = 1
8000 = x² - 20x
x² - 20x - 8000 = 0
x² - 40x + 20x - 8000 = 0
x(x-40) + 20(x-40) = 0
(x-40) (x+20) = 0
x = 40 or -20
So x = 40 km/h [speed is not in negative. So, we do not x = -20]
Therefore the speed of the first car = 20 km/h[x-20 = 40-20=20km/h]
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