SOLUTION: Can you help me set up a rational equation to solve this word problem algebraically please? If a boat goes downstream 78 miles in 3 1/4 hours and upstream 72 miles in 7 1/5 hou

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Question 882369: Can you help me set up a rational equation to solve this word problem algebraically please?
If a boat goes downstream 78 miles in 3 1/4 hours and upstream 72 miles in 7 1/5 hours. Find the speed of the boat in still water and the speed of the current.
Thank you.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
r = boat speed without current
c = current speed
RT=D rate time distance for uniform travel.

________________speed_________time_______distance_______EQUATIONS
Downstream______r+c___________3%261%2F4________78___________%28r%2Bc%29%283%261%2F4%29=78
Upstream________r-c___________7%261%2F5________72___________%28r-c%29%287%261%2F5%29=72

The two equations are linear in r and c. Solve the system for r and c. Not much in the way of rational equations. Just a system of two linear equations.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Can you help me set up a rational equation to solve this word problem algebraically please?
If a boat goes downstream 78 miles in 3 1/4 hours and upstream 72 miles in 7 1/5 hours. Find the speed of the boat in still water and the speed of the current.
Thank you.
Let speed of boat in still water, and speed of current be S, and C, respectively
Then: S+%2B+C+=+78%2F%283%261%2F4%29___S+%2B+C+=+78%2F%2813%2F4%29___S+%2B+C+=+78+%2A+%284%2F13%29_____S + C = 24 ----- eq (i) 

Also, S+-+C+=+72%2F%287%261%2F5%29____S+-+C+=+72%2F%2836%2F5%29____S+-+C+=+72+%2A+5%2F36______S – C = 10 ----- eq (ii)
 
Add eqs (ii) & (i) to determine S, or the speed of the boat in still water. Then substitute value for S in
EITHER eq (i) or (ii) to determine C, or speed of current.
Then do a check!!

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