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Question
A girl goes to her friend’s house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x + 2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, find ‘x’.
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Solution
We know
`"Time" = "Distance"/"Speed"`
Given, the girl covers a distance of 6 km at a speed x km/hr.
Time taken to cover first 6 km = `6/x`
Also, the girl covers the remaining 6 km distance at a speed (x + 2) km/hr.
Time taken to cover next 6 km = `6/(x + 2)`
Total time taken to cover the whole distance = 2 hrs 30 mins
= `2 30/60`
= `2 1/2`
= `5/2` hrs
`∴ 6/x + 6/(x + 2) = 5/2`
`(6x + 12 + 6x)/(x(x + 2)) = 5/2`
`(12 + 12x)/(x^2 + 2x) = 5/2`
24 + 24x = 5x2 + 10x
5x2 – 14x – 24 = 0
5x2 – 20x + 6x – 24 = 0
5x(x – 4) + 6(x – 4) = 0
(5x + 6)(x – 4) = 0
`x = (-6)/5, 4`
Since, speed cannot be negative.
Therefore, x = 4.
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