Answer:
The distance the marina can travel = [tex]x_{}[/tex] = 48 miles
Step-by-step explanation:
The rate going out against the current is = u - v = 20 [tex]\frac{mi}{h}[/tex]
The rate going out with the current is = u + v = 30 [tex]\frac{mi}{h}[/tex]
Let the distance traveled by the motorboat = [tex]x_{}[/tex]
Total time the boat can travel = 4 hours
⇒ Total time = ( Time taken by boat to go against the current ) + ( Time taken by boat to go with the current )
⇒ 4 = [tex]\frac{x}{u - v} + \frac{x}{u + v }[/tex]
⇒ 4 = [tex]\frac{x}{20} + \frac{x}{30}[/tex]
⇒ 4 = [tex]\frac{x}{12}[/tex]
⇒ [tex]x_{}[/tex] = 48 miles
This is the distance the marina can travel.
