A ship traveled 120 km with the current, and then turned around and traveled back, spending 5h and 24 min on its trip. Find the speed of the current if the speed of the ship in still water is 45 km/hour.

Answer 1

speed of current --- x km/h

speed with the current = x+45 kmh
speed against the current = 45-x km/h

120/(45-x) + 120/(45+x) = 27/5 , (5hrs, 24 min = 5 + 24/60 hrs = 27/5 hrs)
multipply each term by 5(45+x)(45-x)
600(45+x) + 600(45-x) = 27(45+x)(45-x)

expand and arrange as a standard quadratic equation
and solve using your favourite method

You will get 2 nice answers, one is negative, clearly you would choose the
positive answer.

Answer 2

you should try and solve the problem yourself, because it is good practice, but if you want to double check your work the answers the quadratic formula are 5 and -5, but -5 doesn't fit our domain, since this is a word problem, so the answer is 5 km/h.

Answer 3

5 km/h