SOLUTION: A motorboat travels 130 km in 5 hours going upstream. It travels 270 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rat

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Question 997437: A motorboat travels 130 km in 5 hours going upstream. It travels 270 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
This form of question is so common, it will be solved here only symbolically. 

KNOWN VARIABLES
system%28n=distanceUpStream%2Cp=distanceDownStream%2Ct=timeEachWay%29
UNKNOWN VARIABLES
system%28r=boatSpeed%2Cc=speedOfCurrent%29

VARIABLES' ASSIGMENTS
system%28n=130%2Cp=270%2Ct=5%29

                speed        time       distance
UPSTREAM        r-c           t          n
DOWNSTRM        r+c           t          p

RT=D shows travel rates rule for uniform rate, relating rate time and distance.

system%28%28r-c%29t=n%2C%28r%2Bc%29t=p%29

system%28rt-ct=n%2Crt%2Bct=p%29

system%28tr-tc=n%2Ctr%2Btc=p%29 , notice that terms are arranged so known coefficient on left
and unknown variable on the right, IN EACH TERM, in the left members.



Elimination Method can be used as a start.
tr-tc%2Btr%2Btc=n%2Bp
2tr=n%2Bp
highlight%28r=%28n%2Bp%29%2F%282t%29%29

tr-tc-tr-tc=n-p
-2tc=n-p
2tc=p-n
highlight%28c=%28p-n%29%2F%282t%29%29

Substitute the given assigned values to evaluate r and c.

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

A motorboat travels 130 km in 5 hours going upstream. It travels 270 km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Let speed of boat, in still water be S, and speed of current, C

Then total upstream speed = S - C, and total downstream speed = S + C

We then get: S+-+C+=+130%2F5______S – C = 26 ------- eq (i)

S+%2B+C+=+270%2F5_____S + C = 54 ------- eq (ii)

2S = 80 ------- Adding eqs (ii) & (i)

S, or speed of boat, in still water = 80%2F2, or highlight_green%2840%29 km/h

40 + C = 54 --------- Substituting 40 for S in eq (ii)

C, or speed of current = 54 – 40, or highlight_green%2814%29 km/h