Answer:
You can use A and B systems
Step-by-step explanation:
Lets call z the total speed of the boat. If the boat goes against the current, then, the current will drop the boat natural speed, and therefore z is obtained from substracting y from the rate of the boat on still water, x. Thus, z = x-y. If The boat goes in favor of the current, then the current will raise the speed, and we obtain z by adding y to x. If we want to calculate x and y, we know that:
On the first trip, z = x-y, and it took 6 hours to finish the 120 mile trip, therefore 6z = 120, or equivalently, 6(x-y)=120
On the return trip, z = x+y, and it took 5 hours to finish the trip, so we have 5z = 5(x+y) = 120.
Thus, in order so solve the problem, we can use system A and B.
Note that system A is equivalent to the equation x-y = 20, obtained by dididing everything by 6. If we divide by 5 the second equation we obtain that x+y = 24. We have
By summing this equations it follows that 2x = 44, therefore x = 22. Since x-y = 20, we obtain that y = 2.
