Aspire Faculty ID #16601 · Topic: NIMCET 2008 · Just now
NIMCET 2008

A person travels on a cycle from home to church on a straight road with wind against him. He took 4 hours to reach there. On the way back he took 3 hours as wind was in the same direction. If there is no wind, how much time does he take to travel from home to church?

Solution

Let speed in still air $=v$, wind speed $=w$, distance $=d$.
Against wind: $d=(v-w)\cdot 4$
With wind: $d=(v+w)\cdot 3$
So $4v-4w=3v+3w \Rightarrow v=7w$
Then $d=(7w-w)\cdot 4=24w$
No wind time $=\dfrac{d}{v}=\dfrac{24w}{7w}=\dfrac{24}{7}$ hr
$=\ 3$ hr $+\dfrac{3}{7}$ hr $=3$ hr $25$ min $42$ sec (approx)

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