Multiple choice

A car travels a distance of 840 km at a uniform speed. If the speed of the car is increased by 10 km/hr, it takes two hours less to cover the same distance. What is the original speed of the car?

  1. 45 km/hr

  2. 50 km/hr

  3. 60 km/hr

  4. 75 km/hr

  5. 80 km/hr
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C Correct answer
Explanation

Let original speed be v. 840/v - 840/(v+10) = 2. 420/v - 420/(v+10) = 1. 420(v+10-v) = v(v+10). 4200 = v^2 + 10v. v^2 + 10v - 4200 = 0. (v+70)(v-60) = 0. Since speed > 0, v = 60.

AI explanation

Using the Time, Speed and Distance formula, let the original speed be v km/hr. The original time is 840/v and the new time is 840/(v + 10). The difference in time is 2 hours, so we write the equation (840/v) - (840/(v + 10)) = 2. Solving the quadratic equation v^2 + 10v - 4200 = 0 gives v = 60. The original speed of the car is 60 km/hr.

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