Answer: the speed of the current is 6 mph
Step-by-step explanation:
Let x represent the speed of the current.
Logan is driving a boat that has a speed of 18 mph in standing water.
Assuming the current slowed down the boat while she was going up(upstream), it means that his total speed was (18 - x) mph
Also, if the current helped the boat while she was going down(downstream), it means that his total speed was (18 + x) mph
Time = distance/speed
The boat travels 4 miles each way. The time taken to travel upstream is
4/(18 - x)
Time taken to travel downstream is
4/(18 + x)
The round trip took 0.5 hour. It means that
4/(18 - x) + 4/(18 + x) = 0.5
Multiplying through by (18 - x)(18 + x), it becomes
4/(18 - x) + 4/(18 + x) = 0.5(18 - x)(18 + x)
4(18 + x) + 4(18 - x) = 0.5(18 - x)(18 + x)
72 + 4x + 72 - 4x = 0.5(324 + 18x -
18x - x²)
144 = 0.5(324 - x²)
144 = 162 - 0.5x²
0.5x² = 162 - 144
0.5x² = 18
x² = 18/0.5 = 36
x = √36
x = 6
