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A train travels a distance of 300 km at a constant speed. If the speed of the train is increased by 5 km per hour .The journey would have taken 2 hours less. Find the speed of the train?
Wiki User
∙ 14y ago
You can express that problem as an equation where 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.
We can say then that the train was moving at twenty-five kilometers per hour.
Wiki User
∙ 14y ago
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