A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. What is the rate of the current?

1 Answer
Apr 26, 2016

The current is flowing at #5# miles/hour.

Explanation:

Let #b# be the speed of the boat (relative to the water)
and #c# be the speed of the water. (both in miles/hr.)

We are told
#color(white)("XXX")color(red)(3(b+c)=120)#
and
#color(white)("XXX")color(blue)(4(b-c)=120)#

therefore
[1]#color(white)("XXX")color(red)(b+c=40)#
and
[2]#color(white)("XXX")color(blue)(b-c=30#

Subtracting [2] from [1]
[3]#color(white)("XXX")color(green)(2c=10)#
#rArrcolor(white)("XXX")color(green)(c=5)#