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Question
A car travels a distance of 72 km at a certain average speed of x km per hour and then travels a distance of 81 km at an average speed of 6 km per hour more than its original average speed. If it takes 3 hours to complete the total journey then form a quadratic equation and solve it to find its original average speed.
Solution
`72/x + 81/(x + 6)` = 3
`\implies 24/x + 27/(x + 6)` = 1
`\implies (24(x + 6) + 27x)/(x(x + 6))` = 1
`\implies` x2 – 45x – 144 = 0
`\implies` (x – 48)(x + 3)
`\implies` x = 48 km/hr
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