SOLUTION: Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. Find t

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Question 912719: Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. Find the rate of the current and the rate of the Gertrude was rowing downstream.

I dint understand how to do this problem.
Can you please help me solve this problem.
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates for Travel, RT=D rate time distance

Let r be the rate Gertude would row if no river current
Let c be the rate of the river, the rate of flow of the river current

_________________rate________time__________distance
DOWNSTREAM_______r+c____________4_____________24
UPSTREAM_________2r-c___________4_____________24

Note very carefully, "the rate of the boat in still water was doubled".

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Gertrude rows her boat 24 miles downstream in 4 hours. In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. Find the rate of the current and the rate of the Gertrude was rowing downstream.

Gertrude rows her boat 24 miles downstream in 4 hours.
let boat speed in still water be x
let rate of current be y
t=d/r
24%2F%28x%2By%29+=4
24=4(x+y)
x+y = 6.................................(1)

In order to make the return trip upstream in the same amount of time, the rate of the boat in still water was doubled. = 2x

t upstream = 24%2F%282x-y%29=4

2x-y = 6................................(2)
add (1) & (2)
we get 3x=12
x=4.......speed of boat in still water
speed of current = 2mph
speed of boat upstream = 2*x= 2*4= 8 mph





Find the rate of the current and the rate of the Gertrude was rowing downstream.