For the following problem:(a) identify the unknown quantities and introduce variables to represent them (b) write equations which express the information given in the statement of the problem (c) solve the equations and give the answerAmelia swam 12 kilometres upstream in 6 hours. The return trip downstream took 2 hours. Find the speed of the current in the river

(a) identify the unknown quantities and introduce variables to represent themAnswer:Distance traveled by Amelia upstream is 12 km. Let us call it x.So that x = 12 kmDistance traveled downstream is unknown. But by reading and understanding the question, one can tell that the distance covered on trip downstream must be the same as distance traveled while going upstream. Let us call it y.So that y = x = 12 kmy = 12 kmSpeed of Amelia while swimming = sSpeed of the current in the river = c(b) write equations which express the information given in the statement of the problemAnswer:s - c = 2 ------eq-1s + c = 6 ------eq-2Step-by-step explanation:Speed of Amelia's swimming is same then why is the time taken while going upstream different than while going downstream?It is because the resistance of current in the river is in the downward direction. It explains why Amelia takes more time to go upstairs and much less to come back.Using Speed = Distance traveled/Time While going upstream:Amelia is going against the current, hence the direction for Amelia and river's current is opposite. We get the equation:s - c = 12/6 = 2------eq-1  where t = 6 hoursWhile going downstream:Amelia is going with the current, hence the direction for Amelia and river's current is same. We get the equation:s + c = 12/2 = 6------eq-2  where t = 2 hours (c) solve the equations and give the answerAnswer:speed of the current in the river  = c = 4 km/hStep-by-step explanation:To find = c?We will use the two equations:s - c = 2 ------eq-1s + c = 6 ------eq-2From eq-1 :[tex]s-c= 2\\⇒  s = 2+c\\[/tex]putting s = 2+c in eq-2:[tex](2+c)+c = 6\\2+2c=6\\2c=8\\c=4[/tex]Hence; the speed of the current of the river is 4 km/h.