QQuestion
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.
✓Answer
In the first case:
Distance = 100 km
Speed = x km/hr
⇒ Time taken = \frac{100}{x} hours
In the second case:
Speed = (x + 5) km/hr
⇒ Time taken = \frac{100}{x+5} hours
The faster journey takes 1 hour less.
⇒ \frac{100}{x}-\frac{100}{x+5}=1
⇒ \frac{100(x+5)-100x}{x(x+5)}=1
⇒ \frac{500}{x²+5x}=1
⇒ x² + 5x = 500
⇒ x² + 5x − 500 = 0
⇒ x² + 25x − 20x − 500 = 0
⇒ x(x + 25) − 20(x + 25) = 0
⇒ (x − 20)(x + 25) = 0
⇒ x = 20 or x = −25
Speed cannot be negative.
Therefore, the original speed is 20 km/hr.
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