Question

A man travels a distance of 196 km by train and returns in a car which travels at a speed of 21 km/hr more than the train. If the total journey takes 11 hours then the average speed of the car is

Answer 1

HEY DEAR ... ✌️


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Let the speed of the train is x km/hr

Given, the car travels at a speed of 21 km/hr faster than the train,

So, the speed of the car = x + 21 km/hr

Now, Time = distance/speed

Again, the man travels a distance of 196km by train and returns in a car and total journey takes 11 hours,

So, 196/x + 196/(x + 21) = 11

=> 196{1/x + 1/(x + 21)} = 11

=> 196{(x + 21 + x)/x*(x + 21)} = 11

=> 196{(2x + 21)/x*(x + 21)} = 11

=> 196(2x + 21) = 11x*(x + 21)

=> 392x + 4116 = 11x2 + 231x

=> 11x2 + 231x - 392x - 4116 = 0

=> 11x2 - 161 x - 4116 = 0

=> 11x2 - 308 x + 147x - 4116 = 0

=> 11x(x - 28) + 147(x - 28) = 0

=> (x - 28)*(11x + 147) = 0

=> x = 28, -147/11

Since speed can not be negative,

So, x = 28

Now, the speed of the car = x + 21 = 28 + 21 = 49 km/hr

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HOPE , IT HELPS ... ✌️