SOLUTION: A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. If the current of the river is 3miles per hour, complete the chart below and u

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. If the current of the river is 3miles per hour, complete the chart below and u      Log On


   

Question 40797This question is from textbook Beginning Algebra
: A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. If the current of the river is 3miles per hour, complete the chart below and use it to find the speed of the boat in still water.
distance = rate * time
UPSTREAM 9 r-3
DOWNSTREAM 11 r+3 This question is from textbook Beginning Algebra

Found 3 solutions by stanbon, josmiceli, VickyFM:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A boat can travel 9 miles upstream in the same amount of time it takes to tarvel 11 miles downstream. If the current of the river is 3miles per hour, complete the chart below and use it to find the speed of the boat in still water.
distance = rate * time
UPSTREAM 9 r-3
DOWNSTREAM 11 r+3
Time= distance/rate
EQUATION:
Time up = Time down
9/(r-3)=11/(r+3)
Cross-multiply to get:
9r+27=11r-33
2r=60
r=30 mph (speed of the boat in still water)
Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
r = rate of boat in still water
t = time for both trips
For upstream
9 = (r-3)t
for downstream
11 = (r+3)t
solve each for r
r-3 = 9/t
r = 9/t + 3
--------------
r+3 = 11/t
r = 11/t - 3
I'll plot these equations, t on the horizontal axis, r on the vertical.
+graph%28+500%2C+300%2C+-.5%2C+2%2C+-2%2C+32%2C+9%2Fx+%2B3%2C+11%2Fx+-+3%29+
It looks like the times are equal when r is about 30 mph, the rate of
boat in still water.
check
r = 9/t + 3
r = 11/t - 3
30 = 9/t + 3
27 = 9/t
27t = 9
t = 1/3 hr
-------------
30 = 11/t - 3
33 = 11/t
33t = 11
t = 1/3 hr
OK

Answer by VickyFM(4) About Me  (Show Source):
You can put this solution on YOUR website!
When an object goes upstream it needs more effort. If you do not give it effort it loses speed or goes back. We use subtraction. When an object goes downstream it moves fast and speed increases so we use addition.
Upstream: (r-3)
Downstream:(r+3)
upstream:(r-3)/9
downstream: (r+3)/11
What we must do now is cross multiply:
We have
(r-3)/9=(r+3)/11
When we cross multiply we now have:
11(r-3)= 9(r+3)
Distribute:
11r-33=9r+27
2r=60
r=30