Multiple choice

Last Saturday Keshav visited his friend who lived in a village on his motorbike. Part of the distance was on mud road which he covered at 16 km/h, whereas the remaining was on gravel which he covered at a speed which was 9 km/h more than that on mud road. If he covered a total distance of 90 km in four and a half hours, for how long (in hours) did he travel on gravel?

  1. 1.5

  2. 2

  3. 2.5

  4. 2.25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let mud distance be d1, gravel distance be d2. d1 + d2 = 90. Time t1 + t2 = 4.5. Speed v1 = 16, v2 = 16 + 9 = 25. d1/16 + d2/25 = 4.5. Substitute d1 = 90 - d2: (90 - d2)/16 + d2/25 = 4.5. (2250 - 25d2 + 16d2) / 400 = 4.5. 2250 - 9d2 = 1800. 9d2 = 450. d2 = 50. Time on gravel = 50 / 25 = 2 hours.

AI explanation

The speeds on mud and gravel are 16 km/h and 25 km/h respectively, since 16 + 9 = 25. Let the time spent on gravel be t hours, so the time on mud is 4.5 - t hours. The equation for total distance becomes 16(4.5 - t) + 25t = 90. Expanding gives 72 - 16t + 25t = 90, which simplifies to 9t = 18, and therefore t = 2 hours.

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