Question

36. A man travels 200 km partially by train and partially by car. If he travels
120 km by train and rest by car he takes 3 hours. But if he travels 80 km by
train and 120 km by car he takes 10 minutes less. Find the speed of the train
and that of the car.​

Answer 1

Answer:

The speed of the train is 60 kmph and the speed of the car is 80 kmph

Step-by-step explanation:

Given :

• A man travels 200 km partially by train and partially by car.
• If he travels  120 km by train and rest by car he takes 3 hours.
• But if he travels 80 km by  train and 120 km by car he takes 10 minutes less.

To find :

the speed of the train and car

Formula :

Speed = distance covered/time taken

⇒ Time taken = distance covered/speed

Solution :

Let the speed of the train be x kmph and that of car be y kmph

Case - (i) :

When he travels  120 km by train and rest by car, he takes 3 hours.

• distance travelled by train = 120 km
• distance travelled by car = 200 - 120 = 80 km

time taken by him to travel 120 km by train = 120/x hours

time taken by him to travel 80 km by car = 80/y hours

total time taken = 3 hours

$\sf \dfrac{120}{x}+\dfrac{80}{y}=3$  ---[1]

Case - (ii) :

When he travels 80 km by  train and 120 km by car, he takes 10 minutes less.

• distance travelled by train = 80 km
• distance travelled by car = 120 km

time taken by him to travel 80 km by train = 80/x hours

time taken by him to travel 80 km by car = 120/y hours

total time taken = 3 hours - 10 min

= 3 hours - 10/60 hours

= (3 - 1/6) hours

= 17/6 hours

$\sf \dfrac{80}{x}+\dfrac{120}{y}=\dfrac{17}{6}$ ---[2]

Put 1/x = a and 1/y = b in both equations,

120a + 80b = 3 ---[3]

80a + 120b = 17/6 ---[4]

Multiply equation [3] by 2 and equation [4] by 3,

240a + 160b = 6 ---[5]

240a + 360b = 17/2 ---[6]

Subtracting equation [5] from [6], we get

360b - 160b = 17/2 - 6

 200b = (17 - 12)/2

 200b = 5/2

  b = 5/400

  b = 1/80

Substitute b = 1/80 in equation [3],

120a + 80b = 3

120a + 80(1/80) = 3

120a + 1 = 3

120a = 3 - 1

120a = 2

 a = 2/120

a = 1/60

__________________

• 1/x = a

1/x = 1/60

x = 60 kmph

• 1/y = b

1/y = 1/80

y = 80 kmph

Therefore, the speed of the train is 60 kmph and the speed of the car is 80 kmph