The current of a river is 4 miles per hour. A boat travels to a point 30 miles upstream and back in 4 hours. What is the speed of the boat in still water?

Answer 1

river current = 4 mph

30 miles up and back in 4 hours

boat speed in still water = b

distance = rate of speed times time traveled

2(30) = downstream speed times time t + upstream speed

times 4 hours - time t

60 = (b+4)t + (b-4)(4-t)

60= bt +4t -bt +4b +4t -16

combine like terms

76 = 8t + 4b

divide by 4

19 = 2t + b where t = time going downstream

average speed = 60/4 = 15 mph

average speed is a weighted average with more weight on the upstream speed as it takes longer. It's weighted by the time.

boat's speed in still water= slightly more than the average speed. b>15 b = 17 mph

19= 2t+17

2=2t

t =2/2 =1 hour going at 17+4 = 21 mph down stream

and 3 hours going 17-4 = 13 mph up stream

60 = 21(1) + 3(13) =21+39 = 60 miles total up and back

average speed = 15 = [(17+4)1 + 3(17-4)]/4

it's a weighted average with 3 times the weight on 13 mph than on 21 mph