Question

in winter a train travels a distance of 264 km at a certain speed .In summer it travels 8 kmph faster than in winter and takes 22mins less than in winter . Find its speed in winter

Answer 1

Answer:

speed =distance*time

Answer 2

Recall:

$\text {Time} = \dfrac{\text{Distance}}{\text{Speed}}$

Define x:

Let the speed in winter be x km/h

In Winter:

Distance = 264 km

Speed = x km/h

$\text {Time taken} = \dfrac{264}{x} \text { hour}$

In Summer:

Distance = 264 km

Speed = (x + 8) km/h

$\text {Time taken} = \dfrac{264}{x + 8} \text { hour}$

Convert the time into hour:

$\text {22 mins} = \dfrac{22}{60} \text { hour}$

$\text {22 mins} = \dfrac{11}{30} \text { hour}$

Solve x:

It takes 22 mins lesser to travel in summer than in winter:

$\dfrac{264}{x} - \dfrac{264}{x+8} = \dfrac{11}{30}$

$\dfrac{264(x + 8) - 264x}{x(x + 8)} = \dfrac{11}{30}$

$\dfrac{264x - 264x + 2112}{x(x + 8)} = \dfrac{11}{30}$

$\dfrac{2112}{x(x + 8)} = \dfrac{11}{30}$

$30 \times (2122) = 11x(x + 8)$

$63360 = 11x^2 + 88x$

$11x^2 + 88x - 63360 = 0$

$11(x + 80)(x - 72) = 0$

$x = 72 \text{ or } x = -80 \text{ (rejected)}$

Find the speed in winter:

Speed in winter = x km/h

Speed in winter = 72 km/h

Answer: 72 km/h