Multiple choice

The distance between station A and B by road is 240 km and by train it is 300 km. A car starts from station A with a speed of x km/hr whereas a train starts from station B with a speed 20 km/hr more than the speed of the car. If the time taken by the train is 1 hour less than that taken by the car, then the quadratic equation formed is:

  1. x2 + 80x - 6000 = 0

  2. x2 + 80x - 4800 = 0

  3. x2 + 240x - 1600 = 0

  4. x2 - 80x + 4800 = 0
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time for car = 240/x. Time for train = 300/(x+20). Given 240/x - 300/(x+20) = 1. 240(x+20) - 300x = x(x+20). 240x + 4800 - 300x = x^2 + 20x. x^2 + 80x - 4800 = 0.

AI explanation

Using the formula time equals distance divided by speed, the time taken by the car is 240 divided by x and the time taken by the train is 300 divided by (x + 20). Since the train takes 1 hour less than the car, we write 300 divided by (x + 20) equals (240 divided by x) minus 1. Multiplying by x(x + 20) gives 300x equals 240x + 4800 minus x squared minus 20x, which rearranges to x squared + 80x - 4800 equals 0.

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