Question

anyone answer this question for me.this question is from lesson 3 maths .class 10

Answer 1

Hey

Here is your answer,

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

Hope it helps you!