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Question
Some school children went on an excursion by a bus to a picnic spot at a distance of 300 km. While returning, it was raining and the bus had to reduce its speed by 5 km/hr and it took two hours longer for returning. Find the time taken to return.
Solution
Distance = 300 km
Let the original speed of the bus be x km/hr
While returning, speed of the bus = (x – 5) km/hr
From the given information, we have
`300/(x - 5) - 300/x = 2`
`(300x - 300x + 1500)/(x(x - 5)) = 2`
`750/(x(x - 5)) = 1`
x2 – 5x – 750 = 0
x2 – 30x + 25x – 750 = 0
x(x – 30) + 25(x – 30) = 0
(x – 30)(x + 25) = 0
x = 30, –25
Since, speed cannot be negative.
So, x = 30.
Speed of the bus while returning = 25 km/hr.
Time taken by the bus to return = `300/25` hrs = 12 hrs.
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