SOLUTION: Mia's motorboat took 3hr. to make a trip downstream with a 6-mph current. The return trip against the same current took 5hr. Find the speed of the boat in still water.

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Question 171131: Mia's motorboat took 3hr. to make a trip downstream with a 6-mph current. The return trip against the same current took 5hr. Find the speed of the boat in still water.
Answer by solver91311(24713) About Me  (Show Source):
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Let r be the speed of the boat in still water. If the current is 6 mph, then the speed of the boat upstream must be r-6 and the speed of the boat downstream must be r%2B6.

Since d=rt, or put another way r=d%2Ft, the upstream trip can be described as r-6=d%2F5 and the downstream trip can be described as r%2B6=d%2F3

Solve both equations for d:

r-6=d%2F5
5r-30=d

r%2B6=d%2F3
3r%2B18=d

Since we have two expressions involving r, the speed of the boat in still water, both equal to d, the distance travelled, set the two expressions equal to each other.

5r-30=3r%2B18

And solve:

5r-3r=18%2B30

2r=48

r=24

Check the answer:

Still water speed: 24

Upstream speed: 24-6=18

Upstream distance: d=18%2A5=90

Downstream speed: 24%2B6=30

Downstream distance: 30%2A3=90

Upstream distance equals downstream distance so the answer checks.