SOLUTION: A motorboat travels 343 kilometers in 7 hours going upstream and 819 kilometers in 9 hours going downstream. What is the rate of the boat in still water and what is the rate of the

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Question 1189536: A motorboat travels 343 kilometers in 7 hours going upstream and 819 kilometers in 9 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

b = speed of the boat in still water
c = speed of the current

When the boat goes upstream, the current slows the boat down to a speed of b-c

For the upstream data, we'll plug in the given distance and time to solve for b
distance = rate*time
343 = (b-c)*7
343/7 = b-c
49 = b-c
49+c = b
b = 49+c

When the boat goes downstream, the current speeds up the boat to a speed of b+c

Plug in the distance and time pertaining to the downstream scenario, along with b = 49+c, to solve for c.

Distance = rate*time
819 = (b+c)*9
819 = (49+c+c)*9
819 = (49+2c)*9
819/9 = 49+2c
91 = 49+2c
2c+49 = 91
2c = 91-49
2c = 42
c = 42/2
c = 21
The speed of the current is 21 km per hour.
b = 49+c
b = 49+21
b = 70
The boat's speed in still water is 70 km per hour.

Answer by ikleyn(52848)   (Show Source):
You can put this solution on YOUR website!
.

            This info is to the composer of this problem.

For a flat river, typical rate of the current is usually not more than 5 kilometers per hour.

The rate of the current of 21 km/h is the rate of a mountain river - - - but motorboats do not float mountain rivers.

            This my message is written to save you from blunders.