Multiple choice

A car covers 420 km with a constant speed. If its speed was 10 km per hour more, then it would have taken one hour less to cover the distance. The speed of the car (in km/hr) is

  1. 50

  2. 55

  3. 57

  4. 60
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D Correct answer
Explanation

Let speed be v. Time taken is 420/v. New time is 420/(v+10). Setting the difference to 1 hour: 420/v - 420/(v+10) = 1. Solving the quadratic v^2 + 10v - 4200 = 0 gives v = 60.

AI explanation

Using the formula Time = Distance / Speed, the equation for the given condition is 420/v - 420/(v + 10) = 1. Multiplying by the common denominator yields 420(v + 10) - 420v = v(v + 10), which simplifies to the quadratic equation v squared plus 10v minus 4200 equals 0. Factoring this quadratic equation gives (v + 70)(v - 60) = 0. Since the speed cannot be negative, the speed of the car is 60 km/hr.

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