Question

A man riding on a bicycle covers a distance of $60$ km in a direction of wind and comes back to his original position in $8$ hours. If the speed of the wind is $10$ km/hr, find the speed of the bicycle.

• A. $13$ km/hr
• B. $20$ km/hr
• C. $23$ km/hr
• D. $30$ km/hr

Answer 1

Answer: (B)

$20$ km/hr

Let speed of bicycle be $x$

Then, $\frac{60}{x+10}+\frac{60}{x-10}=8$

$60x-600+60x+600=8(x^2-100)$

$120x=8x^2-800$

$x^2-15x-100=0$
$x^2-20x+5x-100=0$
$(x-20)(x+5)=0$
$x=20,-5$

Speed cannot be negative.

Hence, speed of bicycle is $20$ km/hr