A speedboat drives 3 times the speed of the current. Thus, it travels downriver for 700 miles 3 hours more than it takes to travel upriver for 325 miles. How do you find the speed of the boat in still water?

1 Answer
Sep 10, 2015

Answer:

Speed of boat (in still water)# = 12.5 (" miles")/(" hour")#

Explanation:

Define:
#color(white)("XXX")b#: speed of boat in still water
#color(white)("XXX")c#: speed of current
#color(white)("XXX")s_(down)#: speed of boat going downstream
#color(white)("XXX")s_(up)#: speed of boat going upstream
#color(white)("XXX")t_(down)#: time to go 700 miles downstream
#color(white)("XXX")t_(up)#: time to go 325 miles upstream

#b = 3c# (given)

#s_(down) = 4c# (speed of boat plus speed of current)
#s_(up) = 2c# (speed of boat minus speed of water)

#t_(down) = 700/(s_(down)) = 700/(4c)#
#t_(up) = 325/(s_(up)) = 325/(2c)#

#t_(down) = t_(up) +3# (given)

#700/(4c)=325/(2c)+3#

#rarr 700/4 = 325/2 +3c#

#rarr 3c = 700/4 - 325/2 = 700/4-650/4 = 50/4 = 12.5#

(and remember that the speed of the boat in still water is #3c#)