Answer: Let's call the speed of the boat "b" and the speed of the current "c". We can set up two equations based on the information given:
Downstream: distance = rate × time
78 = (b + c) × 3
Upstream: distance = rate × time
80 = (b - c) × 4
Now we have two equations with two unknowns, which we can solve simultaneously. We can start by simplifying each equation:
78 = 3b + 3c
80 = 4b - 4c
We can solve the second equation for "b" by adding 4c to both sides and then dividing by 4:
80 + 4c = 4b
20 + c = b
Now we can substitute this expression for "b" into the first equation and simplify:
78 = 3(20 + c) + 3c
78 = 60 + 6c
18 = 6c
c = 3
So the speed of the current is 3 km/h. We can use the expression we found for "b" earlier to find the speed of the boat:
b = 20 + c = 20 + 3 = 23 km/h
Therefore, the speed of the boat is 23 km/h.
Explanation: