Question

a man covered a disance of 200km partly by bus and partly by train

Answer 1

write full question

Answer 2

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