Multiple choice

A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist is

  1. 5 km/hour

  2. 6 km/hour

  3. 7 km/hour

  4. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v be the speed. 14/v - 14/(v-1) = -20/60 = -1/3. Solving 14/(v-1) - 14/v = 1/3 leads to 14v - 14v + 14 = v(v-1)/3, so v^2 - v - 42 = 0. Factoring gives (v-7)(v+6) = 0, so v = 7.

AI explanation

Let the original average speed of the cyclist be v km/hour. Using the formula relating speed, distance, and time, the original time taken is 14/v hours. If his speed reduces by 1 km/hour, his new time is 14/(v - 1) hours. The difference in time is 20 minutes or 1/3 of an hour, so 14/(v - 1) - 14/v = 1/3. Solving this equation yields v^2 - v - 42 = 0, which gives the speeds 7 and -6. Therefore, the original average speed is 7 km/hour.

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