A motorboat maintained a constant speed of 21 miles per hour relative to the water in going 14 miles upstream and then returning. The total time for the trip was 1.5 hours. Use this information to find the speed of the current.

a) 3 miles per hour
b) 5 miles per hour
c) 7 miles per hour
d) 4 miles per hour
e) 2 miles per hour

Going downstream the speed of the boat is added to the speed of the water, on the way back it is opposite to it, then the speed of the water is substracted to that of the boat, and we have the total time of the trip, then we can write down a system of equations as follows:

x:=Speed of water that is being asked

t1:= time going downstream

t2:= time going upstream

(21+x)*t1=14 (1)

(21-x)*t2=14 (2)

t1+t2=1.5 (3)

then t1=1.5-t2, replacing this in (1) we have (21+x)*(1.5-t2)=14, then t2=1.5-(14/(21+x)) (4). Doing the same in (2) we get t2=14/(21-x) (5), this way we can use (4) and (5) and get that:

1.5-(14/(21+x))=14/(21-x), doing the operations we get that 588/(441-x^2)=1.5 or equivalently 1.5x^2-73.5=0 or x^2-49=0 or (x-7)(x+7)=0, then the possible answers are x=7 or x= -7, here we consider the positive answer, that in magnitude is the same as the other, because we already considered the direction of the water into the equations. Then the answer is c) 7mph.