NumericalModerate3 marks
A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be ‘x’ km/h, form an equation and solve it to evaluate ‘x’.
Topic: Quadratic word problems
Previous-year question practice database
Answer
Exam answer
Let the original speed be x km/h. Reduced speed = x−10 km/h.
Original time = 240/x. Reduced-speed time = 240/(x−10).
The journey takes 2 hours longer: 240/(x−10) − 240/x = 2.
Multiplying by x(x−10): 240x − 240(x−10) = 2x(x−10)
2400 = 2x² − 20x
x² − 10x − 1200 = 0
(x−40)(x+30)=0.
Since speed is positive: x = 40 km/h.
Answer: 40 km/h.
Explanation
Form the time equation using time = distance/speed. Reject the negative root.
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