Multiple choice

By increasing the speed of the car by $10 km/hr$ the time of journey for a distance of $72 km$ is reduced by $36$ minutes. Find the original speed of the car.

  1. $30 km/hr$
  2. $40 km/hr$
  3. $20 km/hr$
  4. $50 km/hr$
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A Correct answer
Explanation

Let original speed be v. Time taken is 72/v. New time is 72/(v+10). The difference is 36 minutes (0.6 hours). Solving 72/v - 72/(v+10) = 0.6 leads to v^2 + 10v - 1200 = 0. Factoring gives (v+40)(v-30)=0, so v=30.

AI explanation

Let the original speed be x km/hr, so the original time for 72 km is 72/x hours. The new speed is (x+10) km/hr, making the new time 72/(x+10) hours. Using the equation 72/x - 72/(x+10) = 36/60 (since 36 minutes is 0.6 hours), we simplify to get 72(x+10) - 72x = 0.6x(x+10). Solving the quadratic equation 720 = 0.6x^2 + 6x, or x^2 + 10x - 1200 = 0, yields x = 30. The original speed of the car is 30 km/hr.

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