Multiple choice

John is faster than Jude. John and Jude each walk $20$ km. The sum of their speeds is $9$ km/hr and the sum of their time taken is $9$ hrs. Then (iv) What is the time taken by Jude in hours?

  1. $2$ hours
  2. $3$ hours
  3. $4$ hours
  4. $5$ hours
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D Correct answer
Explanation

Let speeds be J and j. J + j = 9. Time = 20/J + 20/j = 9. 20(J+j)/(J*j) = 9 => 20(9)/(J*j) = 9 => J*j = 20. Roots of x^2 - 9x + 20 = 0 are 4 and 5. Since John is faster, John = 5, Jude = 4. Time for Jude = 20/4 = 5 hours.

AI explanation

Using the formula time equals distance divided by speed, let the time taken by John be t hours, so the time taken by Jude is 9 minus t hours. Their speeds are 20 divided by t and 20 divided by 9 minus t, so the equation is 20 divided by t plus 20 divided by 9 minus t equals 9. Multiplying by t times 9 minus t gives 180 equals 9t minus 9t squared, which simplifies to 9t squared minus 9t plus 180 equals 0 or t squared minus 9t plus 20 equals 0. Factoring this quadratic equation gives t equals 4 or 5; since Jude is slower, his time is 5 hours.

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