A car did a journey in t hours. Had the average speed been x \text{ kmph} greater, the journey would have taken y hours less. How long was the journey?

  1. A. x(t-y)ty
  2. B. x(t-y)ty^{-1} ✓
  3. C. x(t-y)ty^{-2}
  4. D. x(t+y)ty

Correct Answer: B. x(t-y)ty^{-1}

Explanation

Let the distance be D. Original speed v = \frac{D}{t}. The new speed is v+x = \frac{D}{t-y}. Substituting v, we get \frac{D}{t} + x = \frac{D}{t-y}. Solving for x gives x = D(\frac{1}{t-y} - \frac{1}{t}) = D[\frac{y}{t(t-y)}]. Thus, D = \frac{xt(t-y)}{y} = x(t-y)ty^{-1}.

Related questions on Arithmetic

Practice more CDS Elementary Mathematics questions