A train covers a distance of $600 k m$ at $x k m / h r$ . had the speed been $(x + 20) k m / h r$ the time taken to cover the same distance would have been reduced by $5 h o u r s$ . Write down an equation in $x$ and solve it to evaluate ' $x$ '.

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Solution

according to the question
$\frac{600}{x} - \frac{600}{x + 20} = 5$
$\frac{600 x + 12000 - 600 x}{x^{2} + 20 x} = 5$
$600 x + 12000 - 600 x = 5 x^{2} + 100 x$
$5 x^{2} + 100 x - 12000 = 0$
$x^{2} + 20 x - 2400 = 0$
$x^{2} + 60 x - 40 x - 2400 = 0$
$x (x + 60) - 40 (x + 60) = 0$
$(x + 60) (x - 40) = 0$
$x = 40 k m / h r$ since speed cannot be negative

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A train covers a distance of 600 km at x km/hr. had the speed been (x+20) km/hr the time taken to cover the same distance would have been reduced by 5 hours. Write down an equation in x and solve it to evaluate 'x'.

according to the question600x−600x+20=5600x+12000−600xx2+20x=5600x+12000−600x=5x2+100x5x2+100x−12000=0x2+20x−2400=0x2+60x−40x−2400=0x(x+60)−40(x+60)=0(x+60)(x−40)=0x=40km/hr since speed cannot be negative

A train covers a distance of $600 k m$ at $x k m / h r$ . had the speed been $(x + 20) k m / h r$ the time taken to cover the same distance would have been reduced by $5 h o u r s$ . Write down an equation in $x$ and solve it to evaluate ' $x$ '.