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.

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) (Show Source): You can put this solution on YOUR website!
Let be the speed of the boat in still water. If the current is 6 mph, then the speed of the boat upstream must be and the speed of the boat downstream must be .

Since , or put another way , the upstream trip can be described as and the downstream trip can be described as

Solve both equations for d:

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

And solve:

Check the answer:

Still water speed:

Upstream speed:

Upstream distance:

Downstream speed:

Downstream distance:

Upstream distance equals downstream distance so the answer checks.
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