Sue rowed her boat across lake and back in 3hrs. Rate returning was 2mph less than the rate of going, the distance each way was 7miles, find her rate of going.

Question

I need to find out the value of r or her rate on her first trip across the lake in miles per hour.

Answer 1

Time = Distance/Rate; let G = rate going so that G-2 = rate returning

 

(7/G) + [7/(G-2)] = 3

 

7G - 14 + 7G = 3G(G-2) = 3G² - 6G

 

3G² - 20G + 14 = 0

 

The quadratic formula gives (20  ± 232^1/2)/6 

 

Take the + radical, gives G = 5.87 and return rate = 3.87

 

The - radical gives an extraneous root.