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Question
A man covers a distance of 100 km, travelling with a uniform speed of x km/hr. Had the speed been 5 km/hr more it would have taken 1 hour less. Find x the original speed.
Solution
Time taken by a man = `100/x` hrs.
Now, New speed of man = (x + 5) km/hr
∴ Time taken by a man = `100/((x + 5))` hrs.
According to question,
`100/x - 100/(x + 5)` = 1 hour
`100[1/x - 1/(x + 5)]` = 1
`100[(x + 5 - x)/(x(x + 5))]` = 1
500 = x(x + 5)
x2 + 5x – 500 = 0
x2 + 25x – 20x – 500 = 0
x(x + 25) – 20(x + 25) = 0
(x + 25)(x – 20) = 0
x = 20 or x = – 25 ...(Speed cannot be negative)
Hence x = 20 km/hour
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