A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going dow

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Assumptions:

• B = the speed of the boat in still water.
• S = the speed of the stream

Relative to the bank, the speeds are:

• Upstream is B - S.
• Downstream is B + S.

Use the Distance equation: Rate * Time = Distance

• Upstream: (B-S)6 = 258
• Downstream: (B+S)6 = 330

Simplify first by dividing each equation by 6:

• B - S = 43
• B + S = 55

Solve this system of equations by elimination. Add the two equations together:
(B + B) + (S - S) = 43 + 55

Cancelling the S's, we get:
2B = 98

Divide each side by 2:
B = 49 mi/hr

Substitute this into either equation and solve for S.
B + S = 55
49 + S = 55

To solve this, we type it in our search engine and we get:
S = 6 mi/hr