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Exemplo 5.43 de Elementary Algebra, 5.4 Solve Applications with Systems of Equations
Solve Applications with Systems of Equations: exemplo 5.43
Problema e solução em inglês, como no livro original.
Translate to a system of equations and then solve:
A river cruise ship sailed 60 miles downstream for 4 hours and then took 5 hours sailing upstream to return to the dock. Find the speed of the ship in still water and the speed of the river current.
Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.
Solução
Read the problem.
This is a uniform motion problem and a picture will help us visualize the situation.
Identify what we are looking for. We are looking for the speed of the ship
in still water and the speed of the current.Name what we are looking for. Let the rate of the ship in still water.
the rate of the currentA chart will help us organize the information.
The ship goes downstream and then upstream.
Going downstream, the current helps the
ship; therefore, the ship’s actual rate is s + c.
Going upstream, the current slows the ship;
therefore, the actual rate is s − c.Downstream it takes 4 hours.
Upstream it takes 5 hours.
Each way the distance is 60 miles.Translate into a system of equations.
Since rate times time is distance, we can
write the system of equations.Solve the system of equations.
Distribute to put both equations in standard
form, then solve by elimination.Multiply the top equation by 5 and the bottom equation by 4.
Add the equations, then solve for s.Substitute s = 13.5 into one of the original equations. Check the answer in the problem.
The downstream rate would be
13.5 + 1.5 = 15 mph.
In 4 hours the ship would travel
15 · 4 = 60 miles.
The upstream rate would be
13.5 − 1.5 = 12 mph.
In 5 hours the ship would travel
12 · 5 = 60 miles.
Answer the question. The rate of the ship is 13.5 mph and
the rate of the current is 1.5 mph.
Sua vez
O Try It do livro logo depois deste exemplo: mesma ideia, outros números. Só a resposta é dada.
Translate to a system of equations and then solve: A Mississippi river boat cruise sailed 120 miles upstream for 12 hours and then took 10 hours to return to the dock. Find the speed of the river boat in still water and the speed of the river current.
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