Question

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 + y) = 120 and 5(x - y) = 120 6x - 5y = 120 and x + y = 120

Answer 1

the formula would be 5(x+y) = 6(x-y) = 120

 so 5(x+y)= 120 and 6(x-y)=120 can be used

Answer 2

Answer: 6(x - y) = 120 and 5(x + y) = 120

Step-by-step explanation:

Here x represents the rate of boat in still water and y represents the rate of stream,

Hence, the speed of boat with the current = x + y miles per hour

And, the speed of boat against the current = x - y  miles per hour

Going against the current, a boat takes 6 hours to make a 120-mile trip.

⇒ $\frac{120}{x-y} = 6$    ( Time = distance/ speed )

⇒ $120 = 6(x-y)$

Again, When the boat travels with the current on the return trip, it takes 5 hours,

⇒ $\frac{120}{x+y} = 5$

⇒ $120 = 5(x+y)$

Therefore, first option is correct.