Going against the current, a boat takes 6 hours to make a 120 -mile trip. When the boat travels with the current on the return trip, It takes 5 hours If \( x= \) the rate of the boat in still water and \( y= \) the rate of the current, which of the following systems could be used to solve the problem? \( 6(x+y)=120 \) and \( 5(x-y)=120 \) \( 6 x-5 y=120 \) and \( x+y=120 \) \( 6(x-y)=120 \) and \( 5(x+y)=120 \)

When trying to set up equations to solve this problem, we start by defining the boat's speed in still water as \( x \) and the current's speed as \( y \). When the boat goes upstream (against the current), it travels at \( (x - y) \), and when it goes downstream (with the current), it travels at \( (x + y) \). The system \( 6(x - y) = 120 \) for the upstream trip shows that in 6 hours the boat covers 120 miles, while \( 5(x + y) = 120 \) for the downstream trip shows it covers the same distance in 5 hours, making it the correct choice for solving the problem. To visualize this better, consider a real-world scenario. Think of a fisherman trying to get to the best fishing spot. He paddles against the current for 6 hours to reach it. On the way back, the current aids him, allowing him to return in just 5 hours. Understanding these rates helps the fisherman plan his trips efficiently, making sure he spends more time catching fish than battling the water!