Math, asked by Cheenubird1234, 1 year ago

A man travels 600 km partly by train and partly by car. It take 8 hrs 40 mins 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 rest by car. Find the speed of the train and the car.

Answers

Answered by sk57193786
37
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Answered by wifilethbridge
14

Answer:

The speed of the train is 80 km/hr and the speed of car is 60 km/hr.

Step-by-step explanation:

Let the speed of train be x

Let the speed of car be y

Case 1

Total Distance = 600 km

He travels 320 km by train

So, Distance traveled by car = 600-320= 280 km

Time = \frac{Distance}{Speed}

Time taken by train = \frac{320}{x}

Time taken by car = \frac{280}{y}

Since we are given that It take 8 hrs 40 mins if he travels 320 km by train and rest by car

So, Total time = 8 hrs 40 mins = 8+\frac{40}{60}=\frac{26}{3}

So, \frac{320}{x}+\frac{280}{y}=\frac{26}{3} ---A

Case 2

Total Distance = 600 km

He travels 200 km by train

So, Distance traveled by car = 600-200= 400 km

Time = \frac{Distance}{Speed}

Time taken by train = \frac{200}{x}

Time taken by car = \frac{400}{y}

Since we are given that  It would take 30 minutes more

So, Total time = 8 hrs 40 mins + 30 minutes = 8+\frac{40}{60} +\frac{30}{60}=\frac{55}{6}

So, \frac{200}{x}+\frac{400}{y}=\frac{55}{6}  ---B

Solve A and  B

\frac{320}{x}+\frac{280}{y}=\frac{26}{3}

\frac{200}{x}+\frac{400}{y}=\frac{55}{6}

Plot the lines on the graph

\frac{320}{x}+\frac{280}{y}=\frac{26}{3}   -- Red line

\frac{200}{x}+\frac{400}{y}=\frac{55}{6}  -- Blue line

Intersection point will provide the solution

Refer the attached figure

Intersection point = (80,60)

So, the speed of the train is80 km/hr and the speed of car is 60 km/hr.

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