a train covers a distances of 90 km at a uniform speed had the speed 15km/h more,it would have - Maths - Quadratic Equations

Question

a train covers a distances of 90 km at a uniform speed had the
speed 15km/h more,it would have taken 30 mintues less for the
journey find the original speed of the train ?

Ankush Jain · Accepted Answer

Let the original speed of the train = x km/hr

Distance to be covered by train = 90 km

$Time taken when train travels with original speed = \frac{90}{x} hr.$

$Time taken when train travels with 15 km/h more speed than the original speed = (\frac{90}{x + 15}) hr.$

According to the question given,

$\frac{90}{x} - \frac{90}{x + 15} = \frac{1}{2} [∵ Time is 30 min ∴ Time = \frac{30}{60} hr = \frac{1}{2} hr]$

$\Rightarrow \frac{90 (x + 15) - 90 x}{x (x + 15)} = \frac{1}{2} \Rightarrow 2 (90 x + 15 \times 90 - 90 x) = x (x + 15) \Rightarrow 2 (15 \times 90) = x^{2} + 15 x x^{2} + 15 x - 2700 = 0 x^{2} + 60 x - 45 x - 2700 = 0 x (x + 60) - 45 (x + 60) = 0 (x - 45) (x + 60) = 0 \Rightarrow x = 45, - 60$

x ≠ –60, speed cannot be negative.

∴ x = 45 km/h is the original speed of the train.

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a train covers a distances of 90 km at a uniform speed .had the speed 15km/h more,it would have taken 30 mintues less for the journey find the original speed of the train ?