Multiple choice

A cyclist started a ride at 8 a.m. and, travelling at a speed of 15 km/h, reached his destination point. The cyclist took a break for 30 minutes and then rode back to the starting point at a speed of 10 km/h. The cyclist reached the starting point at 12:15 p.m. What is the total distance covered by the cyclist?

  1. 25 km

  2. 40 km

  3. 45 km

  4. 50 km

  5. 60 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let D be the distance. Time taken to go = D/15. Time taken to return = D/10. Total time including 0.5 hour break is 4 hours and 15 minutes (4.25 hours). So, D/15 + D/10 + 0.5 = 4.25. Solving gives D/15 + D/10 = 3.75, which leads to (2D + 3D)/30 = 3.75, so 5D = 112.5, D = 22.5. Total distance covered is 2D = 45 km.

AI explanation

The total time from start to return is from 8 a.m. to 12:15 p.m., which is 4.25 hours or 4 hours and 15 minutes. Subtracting the 30-minute break leaves 3.75 hours of riding time. Let the one-way distance be d. Using the formula time equals distance divided by speed, the total riding time is d divided by 15 plus d divided by 10. This equals 3.75, so combining the fractions gives 25d divided by 150 equals 3.75, meaning d is 22.5 km. The total distance covered is twice this amount, which is 45 km.

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