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:
Relative to the bank, the speeds are:
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
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.
- Upstream: (B-S)6 = 258
- Downstream: (B+S)6 = 330
- 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