Current of a Stream relative to a dolphin

Question

A dolphin travels at an average of 10 mi/h in still water. The dolphin travels 75 miles downstream with the east coast current and 75 miles upstream against the east coast current in a total of 18 hours. What is the average speed of the current in this section of the Atlantic Ocean? Round to the nearest tenth.

Answer 1

As the dolphin swims at 10 mph in still water, with a current of speed c, it travels at rate 10+c; against the current, it travels at 10 -c.

Thus, it travels 75 miles with the current in 75/(10+c) and 75 miles against the current in 75/(10-c)

As it swims for 18 hours,

75/(10+c) + 75/(10-c) = 18

Getting a common denominator

75[10+c+10-c]/((10+c)(10-c)) = 18

75(20)/((10+c)(10-c)) = 18

1500/(100-c²) = 18

Multiply both sides by (100-c²)

1500 = 18(100-c²)

18c²= 300

c = √(300/18) = √(50/3) = 5√6/3

Rounded to tenths, c = 4.1