if rowed her boat across lake and back in 3 hrs.if rate returnig was 2mph less then the rate going & distance each way was 7mi find her rate going

Question

need help to get answer

Answer 1

 

The rate going as James calls it is called x mph, the rate returning (why not rate coming, James?) is x - 2 mph. The distance each way was 7 miles.  Using the fact that distance = rate multiplied by time, you get

 

7 = (x)  t  for going portion, where t is the time taken to go across.  You get t = 7/x

 

We know that the total time to go and return was 3 hrs, so return time must be 3-t hours.

 

Again use distance = rate multiplied by time for the return

 

7 = (x-2) (3-t)

 

Substitute for t from above, t=7/x

 

7 = (x-2)(3 - 7/x)

 

7x = (x-2)(3x-7)

 

3x² -13x +14 = 7x

 

3x² -20x +14 = 0

 

Solve the quadratic equation and accept the sensible of the two possible roots.

 

Dr. G.