Multiple choice

A car travels a distance of 300 km at a uniform speed. If the speed of the car is increased by 5 km/h, then it takes 2 hours less to cover the same distance. Find the original speed of the car.

  1. 25 km/h

  2. 30 km/h

  3. 20 km/h

  4. 35 km/h

  5. None of these
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A Correct answer
Explanation

Let speed be v. 300/v - 300/(v+5) = 2. 150/v - 150/(v+5) = 1. 150(v+5) - 150v = v(v+5). 750 = v^2 + 5v. v^2 + 5v - 750 = 0. (v+30)(v-25) = 0. v = 25.

AI explanation

Let the original speed be v km/h, making the original time 300 / v hours. The new time at a speed of v + 5 is 300 / (v + 5) hours, and the difference is 2 hours, giving the equation (300 / v) - (300 / (v + 5)) = 2. Multiplying by v(v + 5) simplifies this to 300v + 1500 - 300v = 2v squared + 10v, or 2v squared + 10v - 1500 = 0. Solving this quadratic equation yields v = 25 km/h. The result is 25 km/h.

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