A boat travels 10 miles with a current of 3 mph and then returns the same distance against a current of 5 mph. If the trip took a total of 7 hours, what is the boats speed in calm water?

Answer 1

distance = rate of speed times time

d=rt

10 =(3+b)t

10 = (b+5)t

10 = (b-5)(7-t)

2 equations 2 unknowns, solve for b, by substitution, elimination. ignore the negative solution

b= about 6.68 mph= boat speed in calm water where c=0 mph

the boat goes about 1 hour down stream, about 10/9.68

and about 10/1.68)(7-9.68) hours upstream, about 5.97 hours