Question

a train travels 100km. if its speed was 95km more it would have reached the station 1 hour early. then find its first speed.​

Answer 1

Given:

Distance = 100 km

Define x:

Let the original speed be x km/h

the new speed is (x + 95) km/h

Find the original time needed:

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

$\text {Time} = \dfrac{\text{100}}{\text{x} } \text { hours}$

Find the new time needed:

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

$\text {Time} = \dfrac{\text{100}}{\text{x + 95} } \text { hours}$

Given that the time needed is 1 hour lesser:

$\dfrac{\text{100}}{\text{x} } - \dfrac{\text{100}}{\text{x + 95} } = 1$

$\dfrac{\text{100(x + 95) - 100x }}{\text{x(x + 95)} } = 1$

$100( x+ 95) - 100x = x (x + 95)$

$100x+ 9500 - 100x = x^2 + 95x$

$x^2 + 95x - 9500 = 0$

$x = \dfrac{- 95 \pm \sqrt{(95)^2 - 4(1)(-9500)} }{2(10}$

$x = 60.926 \text { or } x = -155.926 \text { (Rejected)}$

Find the original speed:

$\text{Original Speed } = x$

$\text{Original Speed } = 60.9 \text { km/h}$

Answer: The original speed is 60.9 km/h