Multiple choice

A truck goes from place A to place B covering a distance 150 km with a uniform speed. Another car, starting from A, at a speed 25 km/hr higher than that of the truck, reaches B, 3 hrs earlier. Find the speed of the truck.

  1. 20 km/hr

  2. 30 km/hr

  3. 25 km/hr

  4. 50 km/hr

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speed of truck be v. Speed of car = v+25. Time truck = 150/v. Time car = 150/(v+25). 150/v - 150/(v+25) = 3. 50/v - 50/(v+25) = 1. 50(v+25-v) = v(v+25). 1250 = v^2 + 25v. v^2 + 25v - 1250 = 0. (v+50)(v-25) = 0. v = 25.

AI explanation

Let the truck's speed be x km/hr; its travel time is 150/x hours. The car's speed is x plus 25, making its time 150/(x plus 25) hours, which is 3 hours less than the truck. The equation 150/x minus 150/(x plus 25) equals 3 simplifies to x squared plus 25x minus 1250 equals 0. Solving this quadratic equation yields x equals 25, so the speed of the truck is 25 km/hr.

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