Multiple choice

A train running with a speed of x km/hr covers a certain distance in y hours. If its speed is increased by 12 km/hr, then it will cover the same distance in 2 hours less than the scheduled time. But if its speed is decreased by 10 km/hr, then it will take 3 hours more than the scheduled time. Which of the following is the correct set of equations representing this situation?

  1. x - 6y = -12; 3x - 10y = -30

  2. 3x - 6y = 30; x - 10y = -12

  3. x - 3y = 12; x - 13y = 30

  4. x - 6y = -12; 3x - 10y = 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Distance D = xy. (x+12)(y-2) = xy => xy - 2x + 12y - 24 = xy => -2x + 12y = 24 => x - 6y = -12. (x-10)(y+3) = xy => xy + 3x - 10y - 30 = xy => 3x - 10y = 30.

AI explanation

Since the distance traveled in all cases is the same, we use the distance formula to equate the scenarios: x multiplied by y. For the increased speed scenario, the distance is (x + 12) multiplied by (y - 2), so setting them equal gives xy = xy + 12y - 2x - 24. Simplifying this equation yields 2x - 12y = -24, which reduces to x - 6y = -12. For the decreased speed scenario, the distance is (x - 10) multiplied by (y + 3), so setting it equal to xy gives xy = xy - 10y + 3x - 30. Simplifying this equation yields 3x - 10y = 30. The correct set of equations is x - 6y = -12 and 3x - 10y = 30.

Keep practicing — related questions