kdaniel & edit said:

I only need the formula from the problem, \(\displaystyle I \ can \ figure\ it \ out \ from \ there.\)

QUESTION:

..., sailboats start singly at 1 minute intervals. Boat B is scheduled to start immediately

following Boat A. The captain of Boat B feels ...his boat can sail 1 km/h faster. What is

the average speed of each boat if Boat B overtakes Boat A ... 4 km from the start?

\(\displaystyle Let \ t \ = \ time \ in \ minutes.\)

\(\displaystyle Let \ the \ rate \ = \ kilometers \ per\ minute.\)

\(\displaystyle Let \ the \ distance \ be \ in \ kilometers.\)

\(\displaystyle . . . . . . . . . . . . .. . . . rate \ \times \ time\ = \ distance\)

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\(\displaystyle Boat \ A . . . \ \frac{4}{t + 1} . . . \ \ (t + 1) \ .. . . . . . . \ 4\)

\(\displaystyle Boat \ B . . . . . \ \frac{4}{t} . . . . . . . . . . \ \ t \ \ . . . . . . . . . . . . . \ 4\)

\(\displaystyle Boat \ B's\ rate \ is \ 1 \ km/hr \ faster \ than \ Boat \ B's \ rate., \ or \ \frac{1}{60} \ km/min \ \ in \ addition.\)

\(\displaystyle Boat \ A's \ rate \ + \frac{1}{60} km/min \ = \ Boat \ B's \ rate.\)

A possible equation:

\(\displaystyle \frac{4}{t + 1} + \frac{1}{60} = \frac{4}{t}\)

Now you may solve this equation . . .

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Observations/hints:

1) After you solve for t, you must plug it into which expressions to calculate the boats' rates?

2) Those rates are in km/min, so if you want rates in km/hour, you must convert those rates

to get the corresponding rates in km/hr.

3) This problem is made relatively more complicated to a solver because there is a

conversion of units needed, say, hours to minutes, or minutes to hours.

\(\displaystyle "I \ only \ need \ the \ formula \ for \ the \ problem \ ,..."\)