2. A person travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car he takes 6 hours 30 minutes. But if he travels 200 km by train and the rest by car he takes half an hour longer. Find the speed of the car and that of the train.

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Answers

2014-06-28T17:11:03+05:30
Let x=train speed
Let y = car speed 

speed = distance / time 
time = distance / speed 

6 hours 30 minutes = 6.5 hours <== 400 km by train ; 200 km by car 
1/2 hour longer = 7 hours <== 200 km by train ; 400 km by car 

Train time + car time = total time 

400 / x + 200 / y = 6.5 <== two equations and two unknowns 
200 / x + 400 / y = 7 . . . . . . solve for x and y 

400y + 200x = 6.5 xy 
200y + 400x = 7 xy 

400y - 6.5 xy = - 200x 
200y - 7xy = - 400x 

y ( 400 - 6.5x) = -200x 
y ( 200 - 7x) = -400x 

y (6.5x - 400) = 200x 
y (7x - 200) = 400x 

y = 200x / (6.5x - 400) 
y = 400x / (7x - 200) . . . note this equation ... for later use 

. . . since both equal y, the difference is zero 

200x / (6.5x - 400) - 400x / (7x - 200) = 0 

200x ( 7x - 200) - 400x (6.5x - 400) = 0 

1400x^2 - 40000x - 2600x^2 + 160000x = 0 

120000 x - 1200 x^2 = 0 

100 - x = 0 

x = 100 km / h <===== train speed 

y = 400x / (7x - 200) . . . see note above 

y = 400 * 100 / (7 * 100 - 200) 

y = 80 km / h <===== car speed
hope i helped u:)
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