A boat traveled downstream a distance of 60 mi and then came right back. If the speed of the current was 8 mph and the total trip took 4 hoursfind the average speed of the boat relative to the water.

Answer 1

60 miles one way, 120 total miles

4 hours total time

current = 8 mph

distance = time times speed

t= time downstream, 4-t= time upstream

t(b+8) = 60 = (4-t)(b-8)

-tb +4b + 8t = 60+32

tb + 8t = 60

16t + 4b = 152

4t + b = 38

b = 38-4t

b = 38-4(3/2) = 32 mph = boat speed in still water

(3/2)(32+8) =(3/2)(40) = 60

(4-3/2)(32-8) =(5/2)(24) = 60

You probably want 32 mph for boat speed relative to the water

but also

distance = time times speed

120 = 4b

b = 120/4 = 30 mph = the average speed of the boat.