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.

Answer 1

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