A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance in km is:
35
36$ \dfrac{2}{3} $
37$ \dfrac{1}{2} $
40
Explanation:
Let distance = $ x $ km and usual rate = $ y $ kmph.
Then,$ \dfrac{x}{y} $-$ \dfrac{x}{y + 3} $=$ \dfrac{40}{60} $ $\Rightarrow$ 2 $y \left(y + 3\right)$ = 9$ x $ ....(i) |
And,$ \dfrac{x}{y -2} $-$ \dfrac{x}{y} $=$ \dfrac{40}{60} $ $\Rightarrow$ $y \left(y- 2\right)$ = 3$ x $ ....(ii) |
On dividing (i) by (ii), we get: $ x $ = 40.