A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat? What is the speed of the current?

Let's make boat speed "b" and the river current speed "c".

210 mi / 10 hr = 21 mph down stream (with current)

21 mph = b + c

210 mi / 70 hr = 3 mph up stream (against current)

3 mph = b - c

The distance both ways is the same. (speed*time=distance)

210 mi = 210 mi

10 (b+c) = 70 (b-c)

10b + 10c = 70b - 70c

80c = 60b

80/60 = b/c

4/3 = b/c

this is the ratio of boat speed to current: b = (4/3) c

21 = b + c

21 = (4/3) c + c

21 = (7/3) c

21 (3/7) = c

9 mph = c

3 = b - c

3 = b - 9

12 mph = b

Going down stream the boats going 21 mph and upstream it's 3 miles per hour so the current im guessing is 7 mph