Question

a person Travels 600 km partly by train and partly by car if he covers 400 km by train and the rest by car it takes 6 hour 30 minute but if he travel 200 km by train and the rest by car he takes half an hour longer find the speed of the car and that of train

Answer 1

hello...


Let x=train speed

Let y = car speed

FORMULAS 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

TIME OF TRAIN + TIME OF CAR = total time

400 / x + 200 / y = 6.5 2 eq and 2 unknowns

200 / x + 400 / y = 7 .... solve 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)

the difference is zero

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

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

1400x² - 40000x - 2600x² + 160000x = 0

120000 x - 1200 x² = 0

100 - x = 0

x = 100 km / h speed of train

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

y = 400 × 100 / (7 × 100 - 200)

y = 80 km / h speed of car