Question

A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72km at a average speed os 6kmper hour more than its original speed.if it take 3h to complete the total journey then find its original average speed

Answer 1

A train travels at a certain average for a distance of 63km and then travels a distance of 72km at an average speed of 6km/hr more than its original speed.
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If it takes 3 hours to complete the total journey,what is its original average speed.
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Original-speed DATA:
distance = 63 km ; rate = x km/hr ; time = 63/x hrs.
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Faster-speed DATA:
distance = 72 km ; rate = (x+6)km/hr ; time = 72/(x+6) hrs.
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Equation:
time + time = 3 hrs
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63/x + 72/(x+6) = 3 hrs
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63(x+6) + 72x = 3x(x+6)
21(x+6) + 24x = x(x+6)
45x + 21*6 = x^2+6x
x^2-39x-21*6 = 0
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x^2-39x-126 = 0
(x-42)(x+3) = 0
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Positive solution:
x = 42 km/hr (original rate)

Hope This Helps :)