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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
Time is taken by bus to cover the total distance with speed x km/h = `240/x``
Time taken by bus to cover total distance with speed (x 10) km/h = `240/(x - 10)`
According to the given condition,
`240/(x-10) - 240/x = 2`
`=> 240 (1/(x - 10) - 1/x) = 2`
`=> 1/(x- 10) - 1/x = 1/120`
`=>(x - x + 10)/((x(x-10))) = 1/120`
`=> 10/(x^2 - 10x) = 1/120`
⇒ x2 - 10x = 1200
⇒ x2 - 10x - 1200 = 0
⇒ (x - 40)(x + 30) = 0
⇒ x- 40 = 0 or x = 30 = 0
⇒ x = 40 or x = -30
Since, the speed cannot be negative, the uniform speed is 40 km/h
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