SOLUTION: Please help me with this problem. Write an equation that can be used to solve the problem. Solve the equation and answer the question. A sigh- seeing boat travels at an average sp

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Question 981685: Please help me with this problem.
Write an equation that can be used to solve the problem. Solve the equation and answer the question. A sigh- seeing boat travels at an average speed of 20 miles per hour in the calm water of a large lake. The same boat is used for sigh- seeing in a nearby river. In the river the boat travels 2.9 miles downstream (with the current) in the same amount of time it takes to travel 2.5 miles upstream (against the current)
Find the current of the river.
This is a very large problem and I would be extremely grateful if you could help me.
Found 3 solutions by josgarithmetic, macston, MathTherapy:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
__________________rate__________time__________distance
Lake_______________20
RiverDown_________20+w__________t_____________2.9
RiverUp___________20-w__________t_____________2.5

RT=D uniform travel rates relationship for rate time distance

System of Equations:


ARITHMETIC OR ALGEBRA STEPS
Dividing one entire equation by the other entire equation will eliminate variable t. (This is not the only possible method.)
























about 1.48 mph or about 1.5 mph.


Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
.
c=speed of current
.
time upstream=distance/rate=2.5mi/(20mph-c)
.
time downstream=distance/rate=2.9mi/(20mph+c)
.
Since it takes the same amount of time:
2.5mi/(20mph-c)=2.9mi/(20mph+c) Cross multiply.
(2.5mi)(20mph+c)=(2.9mi)(20mph-c)
50 mi^2/hr+2.5c mi=58mi^2/hr-2.9c mi Subtract 50mi^2/hr from each side.
2.5c mi=8mi^2/hr-2.9c mi Add 2.9c mi to each side.
5.4c mi=8mi^2/hr Divide each side by 5.4 mi.
c=1.48 mi/hr ANSWER: The rate of the current was 1.48 mph.
.
CHECK:
.
2.5mi/(20mph-c)=2.9mi/(20mph+c)
2.5mi/(20mph-1.48mph)=2.9mi/(20mph+1.48mph)
2.5mi/18.52mph=2.9mi/21.48mph
0.135 hr=0.135 hr
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Please help me with this problem.
Write an equation that can be used to solve the problem. Solve the equation and answer the question. A sigh- seeing boat travels at an average speed of 20 miles per hour in the calm water of a large lake. The same boat is used for sigh- seeing in a nearby river. In the river the boat travels 2.9 miles downstream (with the current) in the same amount of time it takes to travel 2.5 miles upstream (against the current)
Find the current of the river.
This is a very large problem and I would be extremely grateful if you could help me.
It's not as "large" or as difficult as you may think!



Let speed of current be C

Total speed when going DOWNSTREAM: 20 + C (boat's speed, plus current's speed)

Total speed when going UPSTREAM:   20 - C (boat's speed, less current's speed)

Time taken to travel 2.9 miles downstream: 

Time taken to travel 2.5 miles upstream: 

Since travel times are equal, we get: 

2.9(20 - C) = 2.5(20 + C) ---------- Cross-multiplying

58 - 2.9C = 50 + 2.5C 

- 2.9C - 2.5C = 50 - 58 

- 5.4C = - 8

C, or speed of current = , or  mph 

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