A motor boat heads upstream a distance of 24 km on a river whose current is running at 3 km per hour. The trip up and back takes 6 hours. Assuming that the motor boat maintained a constant speed, what was its speed?
let the speed of the stream be x km/hour
∴ The speed of the boat upstream = (x - 3) km/hr and the speed of the boat downstream = (x + 3)km/hr
Similarly,
According to the given condition
⇒ 24(x + 3) + 24 (x - 3) = 6 (x + 3) (x - 3)
⇒ 48x = 6x2 – 54
⇒ x2 - 8x - 9 = 0
⇒ x2 - 9x + x – 9 = 0
⇒ x( x - 9) + (x - 9) = 0
⇒ (x + 1) (x - 9) = 0
⇒ x = - 1 or 9
Since the speed of the stream cannot be negative so x = 9 km/hr
Hence the speed of the stream is 9 km/hr.
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