a boat traveled 45 miles downstream (w/ the current) in 3 hours and made the return trip (against the current) in 5 hours. what was the speed of the boat and what was the speed of the current?
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When the boat is travelling in the direction of the current, the velocity of the boat coincides with the velocity of the current, so the net speed of the boat is
c + b
and since it takes 3 hours to travel 45 miles, we have,
3(c+b) = 45 ___(1)
When the boat moves against the current, the velocity of the boat is in the opposite direction, so the net velocity of the boat is
and since it takes 5 hours to travel back 45 miles, we have,
5(c-b) = 45 ___(2)
You have two linear equations in two unknowns, which you can solve.
3c+3b=45 --> c+b=15 ...(3)
5c-5b=45 --> c-b=9 ...(4)
Add (3) to (4):
2c=24 --> c = 12
Subtract (4) from (3):
2b=6 --> b=3.