Question

a train travels a distance of 300 km at constant speed.if the speed of the train is increased by 5 km/hr the journey would have 2 hours less.find the original speed of the train

Answer 1

Hey

Here is your answer,

x is the speed of the train:

300km ÷ x km/h = 300km ÷ (x + 5) km/h + 2h

Then solve the equation for x, recalling that you can treat the units of measurement just like any other variable, manipulating them as necessary:

∴ 300h / x = 300h / (x + 5) + 2h

∴ 300h / x = (300h + 2h[x + 5]) / (x + 5)

∴ 300h(x + 5) = x(300h + 2h[x + 5])

∴ 300hx + 1500h = 300hx + 2hx2 + 10hx

∴ 2hx2 + 10hx - 1500h = 0

∴ x2 + 5x - 750 = 0

∴ (x - 25)(x + 30) = 0

∴ x ∈ {25, -30}

So we know that the speed must have been either twenty-five, or negative thirty kilometers per hour. As the negative value makes no sense in this case, we know that the correct value is twenty five.

Hope it helps you!