Question 286389: Please answer the following story problem. The speed of a boar in still water is 20 mph. If the boar travels 140 miles downstream in the same time that it takes to travel 92 miles upstream, find the speed of the current.
I have the rates s/b downstream 20+x and upstream 20-x But that is the extent right now.
Found 3 solutions by dabanfield, Theo, checkley77:
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! Please answer the following story problem. The speed of a boar in still water is 20 mph. If the boar travels 140 miles downstream in the same time that it takes to travel 92 miles upstream, find the speed of the current.
I have the rates s/b downstream 20+x and upstream 20-x But that is the extent right now.
Good Start!
Distance = rate*time so
Letting t be the common travel time for both trips.
We have for the upstream trip:
1.) 90 = (20-x)*t
and for the downstream trip:
2.) 140 = (20+x)*t
Solving 1.) for t we have:
t = 90/(20-x)
Substituting 90/(20-x) for t in equation 2.) then we have:
140 = (20+x)*(90/(20-x))
To simplify, multiply both sides by (20-x):
140*(20-x)= (20+x)*90
Expand and solve the above for x.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! Rate * Time = Distance.
The time is equal to T.
The distance going upstream is equal to 92 miles.
the distance going downstream is equal to 140 miles.
The speed of the boat in still water is 20 miles per hour.
The speed of the current is x miles per hour.
Going against the current, the net rate of the boat is 20 - x.
Going with the current, the net rate of the boat is 20 + x.
Your 2 equations are going to be:
(20-x)*T = 92
(20+x)*T = 140
If you solve both equations for T, then you get:
T = 92/(20-x)
T = 140/(20+x)
Since both equations equal to T, then they are equal to each other, so you get:
92/(20-x) = 140/(20+x)
Multiply both side of this equation by (20-x) to get:
92 = 140*(20-x)/(20+x)
Multiply both side of this equation by (20+x) to get:
92*(20+x) = 140*(20-x)
Simplify to get:
1840 + 92*x = 2800 - 140*x
Add 140*x to both sides of this equation to get:
1840 + 232*x = 2800
Subtract 1840 from both sides of this equation to get:
232*x = 960
Divide both sides of this equation by 232 to get:
x = 4.137931034
Plug this value for x into the original equations to get:
(20-x)*T = 92
(20+x)*T = 140
Become:
(20-4.137931034)*T = 92
(20+4.137931034)*T = 140
Simplify to get:
15.86206897*T = 92
24.13793103*T = 140
Solve for T in both equations to get:
T = 92/15.86206897 = 5.8 hours
T = 140/24.13793103 = 5.8 hours
Since T is the same for both, the value for x are good.
The speed of the current is 4.137931034 miles per hour.
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! D=RT
140=(20+C)T DOWN STREEM TRIP.
T=140/(20+C)
92=(20-C)T UP STREEM TRIP.
T=92/(20-C)
SET THESE 2 EQUATIONS EQUAL.
140/(20+C)=92/(20-C)
140(20-C)=92(20+C) CROSS MULTIPLY
140(20-C)=92(20+C)
2,800-140C=1,840+92C
-140C-92C=1,840-2,800
-232C=-960
C=-960/-232
C=4.138 SPEED OF THE CURRENT.
PROOF:
140/(20+4.138)=92/(20-4.138)
140/24.138=92/15.862
5.8=5.8
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