A motorboat can maintain a constant speed of 15 miles per hour relative to the water. The boat makes trip upstream to a certain point in 51 minutes; the return trip takes 39 minutes. What is the speed of the current?

Answer:The speed of the current is 2 miles per hours Step-by-step explanation:Given as :The speed of motorboat = x = 15 miles per hourThe time taken by motorboat trip upstream = 51 minutes The time taken by motorboat trip downstream = 39 minutes Let The speed of the current = y miles per hourLet The total distance cover = A milesSo , Speed = [tex]\dfrac{\textrm Distance}{\textrm Time}[/tex]So, x - y = [tex]\dfrac{A}{51}[/tex] I.e  15 - y =  [tex]\dfrac{A}{51}[/tex] And x + y = [tex]\dfrac{A}{39}[/tex] I.e  15 + y = [tex]\dfrac{A}{39}[/tex] [tex]\dfrac{x-y}{x+y}[/tex] = [tex]\dfrac{39}{51}[/tex] I.e [tex]\dfrac{x-y}{x+y}[/tex] = [tex]\dfrac{13}{17}[/tex] Or, 17 × (x - y) = 13 × (x + y)Or, 17 x - 17 y = 13 x + 13 yOr, 17 x - 13 x = 13 y + 17 yOr, 4 x = 30 yNow, ∵ x = 15 miles per hourSo, 4 × 15 = 30 yOr, y =  [tex]\dfrac{60}{30}[/tex] ∴   y = 2 miles per hourHence The speed of the current is 2 miles per hours   Answer