SOLUTION: Traveling at full speed on a river, it takes 4 hours for a motorboat to travel 18 miles upstream and 21 miles downstream. If the current's speed is 2 mph, what is the maximum spee

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Question 1094371: Traveling at full speed on a river, it takes 4 hours for a motorboat to travel 18 miles upstream and 21 miles downstream. If the current's speed is 2 mph, what is the maximum speed of the boat in still water?
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Travel Rates Rule, RT=D to relate speed, time, distance

r, speed of boat when not in a current

r-2, upstream rate
r%2B2, downstream rate
total time, 4 hours 
               SPEED       TIME       DISTANCE
UPSTREAM        r-2       18/(r-2)      18
DOWNSTREAM      r+2       21/(r+2)      21
TOTAL                      4

Total time:
18%2F%28r-2%29%2B21%2F%28r%2B2%29=4

.
.
4r%5E2-39r-10=0
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discriminant=39%5E2%2B4%2A4%2A10=1681=41%5E2
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r=%2839%2B-+41%29%2F8-----must take the positive value

r=80%2F8

highlight%28r=10%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Traveling at full speed on a river, it takes 4 hours for a motorboat to travel 18 miles upstream and 21 miles downstream. If the current's speed is 2 mph, what is the maximum speed of the boat in still water?
Correct answer:

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the unknown speed of the boat in still water.


Then  the effective speed upstream    is x-2  miles per hour,

while the effective speed downstream  is x+2  miles per hour.


The time spent to cover 18 miles upstream is 18%2F%28x-2%29,

while the time to cover 21 miles downstream is 21%2F%28x%2B2%29.


Your time equation is 

18%2F%28x-2%29 + 21%2F%28x%2B2%29 = 4.


To solve it, multiply both sides by (x-2)*(x+2). You will get

18*(x+2) + 21*(x-2) = 4*(x^2-4).


Simplify:

18x + 36 + 21x - 42 = 4x^2 - 16,

4x^2 - 39x + 10 = 0.

Apply the quadratic formula and find the solution x = 10 mph.