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Question
A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be 'x' km/h, form an equation and solve it to evaluate 'x'.
Solution
Distance = 240 km
Let speed of a bus = x km/hr
∴ Time taken = `D/S = (240)/x` hours
Due to heavy rains
Speed of the bus = (x – 10) km/hr
∴ Time taken = `(240)/(x - 10)`
According to the condition,
`(240)/x = (240)/(x - 10) - 2`
`(240)/(x - 10) - (240)/x = 2`
`(240(x - 240x + 2400))/(x(x - 10)) = 2`
`(2400)/(x^2 - 10x) = 2`
`\implies` 2400 = 2x2 – 20x
`\implies` 2x2 – 20x – 2400 = 0
`\implies` x2 – 10x – 1200 = 0
`\implies` x2 – 40x + 30x – 1200 = 0
`\implies` x(x – 40) + 30(x – 40) = 0
`\implies` (x – 40)(x + 30) = 0
Either x – 40 = 0,
Then x = 40
or
x + 30 = 0,
Then x = –30
Which is not possible speed being negative.
∴ Speed of bus = 40 km/h.
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