Question

a man Travels 600 kilometre fastly by train and partly because if we covers 400 kilometre by train in the breast by car it takes in 6 hours and 30 minutes but if he travels 200 km by train and the rest by car and longer find the speed of the train and that of the car plz

Answer 1

Let x = speed of train
Let y = speed of car

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) * 

. . . 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) . from * 

y = 400 * 100 / (7 * 100 - 200)

y = 80 km / h = car speed