Math word problem

Question

A boat travels at a constant speed of 20 miles per hour, relative to the water, as it makes a trip downstream and then returns. If the initial trip downstream takes the boat 30 minutes and the return trip upstream takes the boat 40 minutes, what is the speed of the current?

Answer 1

distance=rate*time

distances are the same

(20+c)(1/2)=(20-c)(2/3)

multiply both sides by 6

3(20+c)=4(20-c)

60+3c=80-4c

3c+4c=80-60

7c=20

c=20/7

c=2 6/7 mph is the speed of the current

check: (22 6/7)(1/2)=(17 1/7)(2/3)

          (160/7)(1/2)=(120/7)(2/3)

          (80/7)=(80/7)  (80/7=11 3/7 miles is the distance traveled)