SOLUTION: Can someone please help me figure this out? Thank you. Alvin paddled for 5 hours with a 3​-km/h current to reach a campsite. The return trip against the same current took

Let  u  be the boat speed in still water (in kilometers per hour, km/h).


Then  the boat's  effective speed downstream is  u+3  km/h,
while the boat's  effective speed upstream   is  u-3  km/h.


    // It is the first major point you need understand and use in this sort of problems.


Now, distance traveled downstream is  5*(u + 3)   (distance = time*effective speed downstream).


Next, distance traveled upstream  is  8*(u - 3)   (distance = time*effective speed upstream)


Distance is the same; so you have this equation


    5*(u + 3) = 8*(u - 3).


    // It is second major point you need understand and use to get the equation.


Simplify and solve for "u" :


    5u + 15 = 8u - 24

    15 + 24 = 8u - 5u

    39 = 3u  ====>  u = 39/3 = 13 km/h.


Thus you just found the boat' speed in still water. It is 13 kilometers per hour.