i need help answering this word problem

Question

Sean started to cross a lake by motorboat. After he had traveled 15 miles, the motor failed and he had to row the remaining 6 miles to shore. His speed by motor was 4 miles per hour faster than his average speed while rowing. If the entire trip took 5.5 hours, what was Sean's average speed while rowing?

Answer 1

Let x = rowing speed

Then, x+4 = speed of boat

 

Distance = (Rate)(Time), so Time = Distance/Rate

 

Time rowing + Time boating = Total Time

 

15/(x+4) + 6/x = 5.5 = 11/2

 

Multiply both sides by the LCD, 2x(x+4)

 

30x + 12(x+4) = 11x(x+4)

 

42x + 48 = 11x² + 44x

 

11x² + 2x - 48 = 0

 

(11x + 24)(x - 2) = 0

 

x = -24/11 or x = 2

 

Since x is the rowing speed, x can't be negative.

 

Therefore, x = 2 mph