Question
A cyclist goes 30 km at speed x km/h and returns 30 km
at speed (x - 5) km/h. Total time taken is 5 hours. Find x.Solution
ATQ, Time going = 30/x Time returning = 30/(x - 5) 30/x + 30/(x - 5) = 5 Multiply by x(x - 5): 30(x - 5) + 30x = 5x(x - 5) 30x - 150 + 30x = 5(x² - 5x) 60x - 150 = 5x² - 25x 0 = 5x² - 25x - 60x + 150 0 = 5x² - 85x + 150 Divide by 5: x² - 17x + 30 = 0 (x - 15)(x - 2) = 0 x = 15 (x must be > 5)
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