SOLUTION: The speed of a stream is 5km/h. If a boat travels 76kms downstream in 2 hrs less time than it takes to travel 54km upstream, what is the speed of the boat in still water. I hav

Question 139479: The speed of a stream is 5km/h. If a boat travels 76kms downstream in 2 hrs less time than it takes to travel 54km upstream, what is the speed of the boat in still water.
I have gotten this far but am not sure if this is correct.
Downstream Boat D= 76km Rate= r+5 Time - t-2. Equation: 76= (r+5) * (t-2)
Upstream Boat D = 54 kms. Rate = r-5 Time = t. Equation 54km= (r-5) *t
To solve Upstream Boat of 54=(r-5)*t = 54= tr-5. Then I divide 54 by 5 to get 10.8. But I am stuck from here and do not think I am on the right track to solving this answer on the speed of the boat. Help would be appreciated. Thanks
Found 2 solutions by frostusna, ankor@dixie-net.com:
Answer by frostusna(7) (Show Source): You can put this solution on YOUR website!
You started correctly and the two equations you obtained are correct.

Now, to eliminate one of the unknowns, solve each equation for t.
, and solving for t gives , and
.
From this we can show that
Rewrite this equation to
To subtract the terms they must have common denominators. To get this we multiply as follows:

Now carry out the multiplication to get:

Carry out the multiplication in the numerator and multiply each term by the denominator to get:

Continuing, you get: . Rewriting becomes:
. Devide through by 2 to simplify. You get
. This is a basic quadratic equation, so using the quadratic equation solver we get:

Solving for r you get two possible solutions:
or or . The correct answer being

I hope this helped.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The speed of a stream is 5km/h. If a boat travels 76kms downstream in 2 hrs less time than it takes to travel 54km upstream, what is the speed of the boat in still water.
:
Here is a better approach. If we write a time equation, we only have 1 unknown
Let r = speed of boat in still water
then
(r-5) = speed upstream
(r+5) = speed downstream
:
Time = dist/speed:
Time upstream - 2 hrs = time downstream
- 2 =
:
Get rid of the denominators, multiply equation by (r+5)(r-5):
(r+5)(r-5)* - 2(r+5)(r-5) = (r+5)(r-5)*
:
Cancel out the denominators:
54(r+5) - 2(r^2-25) = 76(r-5)
:
54r + 270 - 2r^2 + 50 = 76r - 380
:
-2r^2 + 54r - 76r + 270 + 50 + 380 = 0
:
-2r^2 - 22r + 700 = 0
Simplify divide equation by -2 and you have:
r^2 + 11r - 350 = 0
Factor this to:
(r-14)(r+25) = 0
The positive solution:
r = +14 is the speed in still water
:
:
Check solution by finding the time for each:
speed upstream = 9 mph; speed downstream = 19 mph
54/9 = 6 hrs
76/19 = 4
----------
diff = 2 hrs

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