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A train covers a distance of 90kms at a uniform speed. It would have taken 90 minutes less if the speed had been 15km/hr more. Calculate the original duration of the journey.

Posted by Arpit Singla 7 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Naveen Sharma 7 years, 3 months ago

The Questions is it would have taken 30 Minutes less instead of 90 Minutes

Solution:

Let “x” be the usual speed of the train

Let T₁ be the time taken to cover the distance 90 km in the speed x km/hr

Let T₂be the time taken to cover the distance 90 km in the speed (x + 15) km/hr

Time = Distance/Speed

T₁ = $\frac{90}{x}$

T₂ = $\frac{90}{x + 15}$

By using the given condition

T₁ - T₂ = $\frac{30}{60}$

$\frac{90}{x}$ - $\frac{90}{x + 15}$ = $\frac{1}{2}$

Taking 90 commonly from two fractions

$(90 (\frac{1}{x} - \frac{1}{x + 15})) = \frac{1}{2}$

$\frac{x + 15 - x}{(x) (x + 15)} = \frac{1}{2 * 90}$

$\frac{15}{x (x + 15)} = \frac{1}{180}$

$x^{2} + 15 x = 2700$

$x^{2} + 15 x - 2700 = 0 x^{2} + 60 x - 45 x - 2700 = 0 x (x + 60) - 45 (x + 60) = 0 (x + 60) (x - 45) = 0 x + 60 = 0 o r x - 45 = 0 x = 45, - 60$

Speed can't be negative so,

Speed is 45km/h

1Thank You

ANSWER

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