Answer: the speed of the current is 51.85 mph
Step-by-step explanation:
Let x represent the speed of the current.
motorboat maintain a consistent speed of 22 mph relative to the water. Assuming it moved in the direction of the current while going downstream, its total speed would be (22 + x) mph
If it moved against the direction of the current while going downstream, its total speed would be (22 - x) mph
Time = distance/speed
Assuming it went 56 miles upstream and 56 miles downstream, then time taken to go upstream is
56/(22 + x)
Time taken to go downstream is
56/(22 - x)
Since the total trip was 5.5 hours, then
56/(22 + x) + 56/(22 - x) = 5.5
Cross multiplying by (22 + x) and (22 - x), it becomes
56(22 - x) + 56(22 + x) = 5.5[(56 + x)(56 - x)
1232 - 56x + 1232 + 56x = 5.5(3136 - 56x + 56x - x²)
1232 + 1232 = 17248 - 5.5x²
5.5x² = 17248 - 2464 = 14784
x² = 14784/5.5 = 2688
x = √2688
x = 51.85
