Multiple choice

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.

  1. $13$ km/hr
  2. $20$ km/hr
  3. $23$ km/hr
  4. $30$ km/hr
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B Correct answer
Explanation

Let v be the speed of the bicycle. The effective speed with the wind is v + 10 and against the wind is v - 10. The time taken is 60/(v+10) + 60/(v-10) = 8. Solving this quadratic equation: 60(v-10 + v+10) = 8(v^2 - 100), which simplifies to 120v = 8v^2 - 800, or v^2 - 15v - 100 = 0. Factoring gives (v-20)(v+5) = 0, so v = 20 km/hr.

AI explanation

Let the speed of the bicycle be x km/hr, making the downstream speed x plus 10 and the upstream speed x minus 10. Using the formula time equals distance divided by speed, the total time is 60 divided by x plus 10 plus 60 divided by x minus 10, which equals 8 hours. Solving the equation 120x divided by x squared minus 100 equals 8 gives x squared minus 15x minus 100 equals 0. Factoring this quadratic equation yields x equals 20 km/hr.

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