Multiple choice

A man covers a distance of $200$ km travelling with a uniform speed of $x$ km per hour. The distance could have been covered in $2$ hours less, had the speed been $(x + 5)$ km per hour. Calculate the value of $x$.

  1. $20$
  2. $24$
  3. $28$
  4. $32$
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A Correct answer
Explanation

200/x - 200/(x+5) = 2. 100/x - 100/(x+5) = 1. 100(x+5-x) = x(x+5). 500 = x^2 + 5x. x^2 + 5x - 500 = 0. (x+25)(x-20) = 0. x = 20.

AI explanation

Using the time equals distance divided by speed formula, the initial time taken is 200 divided by x and the faster time is 200 divided by (x plus 5). Setting up the equation from the given difference, 200 divided by x equals 200 divided by (x plus 5) plus 2. Solving this quadratic equation gives x equals 20.

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