Question

A man travels 600km apart by train and partly by car. It takes 8 hours and 40 minutes if he travels 320 km by train and rest by car. It would take 30 minutes more if he travels 200 km by train and the rest by the car/. Find the speed of the train and by car separately.


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Answer 1

Answer: The speeds of the train and car are respectively, 80km/ hour and 60 km/ hour.

Explanation: Let x be the speed of the train and y be the speed of the car.

Total distance travelled is 600 km.

The time taken by the man to travel 320 km by train is 320/x

The time taken by the man to travel 280 km by car is 280/y

Hence, the total time taken by the man to travel 600 km is 320/x + 280/y

Given that the total time is 8 hours 40 minutes = 8 2/3 hours = 26/3 hours.

Thus, we have , 320/x + 280/y = 26/3 ....(1)

The time taken by the man to travel 200 km by train is 200/x

The time taken by the man to travel 400 km by car is 400/y

Hence, the total time taken by the man to travel 600 km is 200/x + 400/y

Given that the total time is 30 minutes mire than 8 hours 40 minutes = 8 2/3 hours + 30/60 hour = 26/3 + 1/2 hours

Thus, we have, 200/x + 400/y = 26/3 + 1/2

⇒ 200/x + 400/y 55/6 ...(2)

Substitute, 1/x = u  and 1/y = v

Thus, equations (1) and (2) can be rewritten as,

320u + 280v = 26/3

200u + 400v = 55/6

Solving the above equations, we have,

u = 1/80 and v = 1/60

Thus, the speeds of the train and car are respectively, 80 km/ hour and 60 km/ hour.

Answer 2

Answer:

Speed of Train = 80 km/hr .

Speed of Car = 60 Km/hr .

Explanation:

Let the speed of the Train and Car be 'x' and 'y' respectively .

(Also  let 1/x = u & 1/y = v , This substitution is done make the solution easy)

Case: - 1

In the very first case,

Distance travelled by train = 320 km

Distance travelled by car = 600 - 320

                                          = 280 km

Total time taken = 8 Hours + 40 Minutes

                           = 8 Hours + (40/60) Hours

                           = (8 + 2/3) Hours

                           = (24 + 2)/3 Hours

                           = 26/3 Hours .

Now,

Time taken by travelling by train

= Distance/Speed

= 320/x                                      

= 320u

Time taken in travelling by car

= Distance/Speed

= 280/y

= 280v

Thus,

Total travelling time = 320u + 280v

$\frac{26}{3}=320u+280v\\\;\\\frac{26}{3}=10(32u+28v)\\\;\\\frac{26}{3}=10\times4(8u+7v)\\\;\\\frac{26}{3\times4\times10}=8u+7v\\\;\\\frac{13}{3\times2\times10}=8u+7v\\\;\\8u+7v=\frac{13}{60}\;\;\;\;\;\;\;\;(Equation\;\;i)$

Case:-2

In this case,

Distance travelled by train = 200 km

Distance travelled by car = 600 - 200

                                          = 400 km

Total time taken = 26/3 Hours + 30 minutes

                           = 26/3 Hours + 30/60Hours

                           = (26/3 + 1/2) Hours

                           = (52 + 3)/6 Hours

                           = 55/6 Hours

Now,

Time taken by travelling by train

= Distance/Speed

= 200/x

= 200/x

= 200u

Time taken in travelling by car

= Distance/Speed

= 400/y

= 400v

Thus,

Total travelling time = 200u + 400v

$\frac{55}{6}=200u+400v\\\;\\\frac{55}{6}=100(2u+4v)\\\;\\\frac{55}{6\times100}=2u+4v\\\;\\\frac{11}{6\times20}=2u+4v\\\;\\\frac{11}{120}=2u+4v\\\;\\\text{Multiplying both sides by 4}\\\;\\\frac{11\times4}{120}=8u+16v\\\;\\\frac{11}{30}=8u+16v\\\;\\8u+16v=\frac{22}{60}\;\;\;\;\;\;\;\;(Equation\;\;ii)$

Now Subtracting Equation i) from ii)

16v - 7v = 22/60  - 13/60

9v = 9/60

v = 1/60

1/y = 1/60

y = 60 km / hr

Putting the value of v in equation i)

8u + 7v = 13/60

8u + 7/60 = 13/60

8u = 13/60 - 7/60

8u = 6/60

8u = 1/10

u = 1/80

1/x = 1/80

x = 80 km / hr .