Multiple choice

A car covers a distance of $240$ km with some speed. If the speed is increased by $20$ km/hr, it will cover the same distance in $2$ hours less. Find the speed of the car.

  1. $40$
  2. $45$
  3. $50$
  4. $60$
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A Correct answer
Explanation

Let speed be v. 240/v - 240/(v+20) = 2. 120/v - 120/(v+20) = 1. 120(v+20) - 120v = v(v+20). 2400 = v^2 + 20v. v^2 + 20v - 2400 = 0. (v+60)(v-40) = 0. v = 40.

AI explanation

Let the original speed of the car be x km/hr, so the original time is 240 divided by x hours and the new time is 240 divided by x plus 20 hours. The equation is 240 divided by x minus 240 divided by x plus 20 equals 2. Multiplying by x times x plus 20 gives 4800 equals 2x squared plus 40x, which simplifies to x squared plus 20x minus 2400 equals 0. Factoring this quadratic equation yields x equals 40 km/hr.

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