a man travels 600km apart by train and partly by car. it takes 8 hours 40 min if he travels 320km by train and rest by car. it would take 30min more if he travels 200km by train and rest by car . find the speed of the train and by separately.

speed of train = 94.53 km/h

Speed of car = 59.98 km/h

Step-by-step explanation:

Let x = speed of the train

Let y = speed of the car

The total distance travelled by the man is 600 km. It takes 8 hours 40 min if he travels 320km by train and rest by car. This means that the distance travelled by car is 600 - 320 = 280km

60 minutes = 1 hour

The total time of travel = 8 + (40/60) = 8.67 hours

Total time = total distance/total speed

8.67 = 320/x + 280/y

320/x = 8.67 - 280/y

320/x = (8.67y - 280)/y

Cross multiplying, it becomes

320y = x(8.67y - 280)

y = x(8.67y - 280)/320- - - - - - - - - - -1

it would take 30min more if he travels 200km by train and rest by car. The total time would be 8.67 + 0.5 = 9.17 hours

Distance covered by the car is 600 - 200 = 400 km

Therefore,

9.17 = 200/x + 400/y

200/x = 9.17 - 400/y

200/x = (9.17y - 400)/y

Cross multiplying, it becomes

200y = x(9.17y - 400)

y = x(9.17y - 400)/200 - - - - - - - 2

Equating equation 1 to equation 2, it becomes

x(8.67y - 280)/320 = x(9.17y - 400)/200

Dividing both sides by x, it becomes

(8.67y - 280)/320 = (9.17y - 400)/200

Cross multiplying, it becomes

200(8.67y - 280) = 320(9.17y - 400)

1734y - 56000 = 2934.4y - 128000

2934.4y - 1734y = - 56000 + 128000

1200.4y = 72000

y = 72000/1200.4

y = 59.98 km/h

Substituting y = 59.98 into equation 1, it becomes

59.98 = x(8.67 × 52.98 - 280)/320

52.98 × 320 = x(459.3366 - 280)

16953.36 = 179.3366x

x = 16953.36/179.3366

x = 94.53 km/h

step-by-step explanation: it is d

b