A motorboat maintain a consistent speed of 22 mph relative to the water and going 56 miles upstream and then returning the total trip was 5.5 hours use this information to find the speed of the current

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