Answer: speed of train = 94.53 km/h
Speed of car = 59.98 km/h
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