Question

a motorboat whose speed is 15 km per hour in still water takes the move to go 24 km upstream then the return downstream to the same spot what is the original speed

Answer 1

the original speed is 18 km per hour

Answer 2

Let the speed of the stream be x km/hr.

Speed of the boat upstream = Speed of the boat in still water - speed of the stream
= (18 - x) km/hr

Speed of the boat downstream = speed of the boat in still water + speed of the stream
=(18 + x)km/hr

Time of upstream journey = time of downstream journey + 1 hr

24km ÷ (18 - x)km/hr = 24 km ÷ (18 + x)km/hr +1

(24 ÷ 18 - x) - (24 ÷ 18 + x) = 1

432 + 24 x - 432 + 24 x  ÷ (18 - x) (18 + x) = 1

x² + 54 x - 6 x - 324 = 0

x (x + 54) - 6 (x + 54) = 0

(x + 54) (x - 6) = 0

x + 54 = 0 , x - 6 = 0

x = - 54 , x = 6

Therefore the original speed is 6 km/hr.