Multiple choice

A cyclist covering a distance of 40 km would have reached 1 hour earlier if he had run at an increased speed of 2 km/hr His speed in (km/hr) was

  1. 6

  2. 8

  3. 10

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speed be v. Time taken is 40/v. If speed is v+2, time is 40/(v+2). We have 40/v - 40/(v+2) = 1. Solving v^2 + 2v - 80 = 0 gives (v+10)(v-8) = 0, so v = 8 km/hr.

AI explanation

Let the original speed be v km/hr and the usual time be t hours; using the formula distance equals speed multiplied by time gives 40 = v * t and 40 = (v + 2) * (t - 1). Substituting t = 40 / v into the second equation gives 40 = (v + 2) * (40 / v - 1), which simplifies to 40v = (v + 2)(40 - v) and further to v^2 + 2v - 80 = 0. Factoring this quadratic equation results in (v - 8)(v + 10) = 0, so the original speed is 8 km/hr.

Keep practicing — related questions