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Example 5.44 from Elementary Algebra, 5.4 Solve Applications with Systems of Equations
Solve Applications with Systems of Equations: example 5.44
Translate to a system of equations and then solve:
A private jet can fly 1095 miles in three hours with a tailwind but only 987 miles in three hours into a headwind. Find the speed of the jet in still air and the speed of the wind.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Read the problem.
This is a uniform motion problem and a picture will help us visualize.
Identify what we are looking for. We are looking for the speed of the jet
in still air and the speed of the wind.Name what we are looking for. Let the speed of the jet in still air.
the speed of the windA chart will help us organize the information.
The jet makes two trips-one in a tailwind
and one in a headwind.
In a tailwind, the wind helps the jet and so
the rate is j + w.
In a headwind, the wind slows the jet and
so the rate is j − w.Each trip takes 3 hours.
In a tailwind the jet flies 1095 miles.
In a headwind the jet flies 987 miles.Translate into a system of equations.
Since rate times time is distance, we get the
system of equations.Solve the system of equations.
Distribute, then solve by elimination.Add, and solve for j.
Substitute j = 347 into one of the original
equations, then solve for w.Check the answer in the problem.
With the tailwind, the actual rate of the
jet would be
347 + 18 = 365 mph.
In 3 hours the jet would travel
365 · 3 = 1095 miles.
Going into the headwind, the jet’s actual
rate would be
347 − 18 = 329 mph.
In 3 hours the jet would travel
329 · 3 = 987 miles.Answer the question. The rate of the jet is 347 mph and the
rate of the wind is 18 mph.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Translate to a system of equations and then solve: A small jet can fly 1,325 miles in 5 hours with a tailwind but only 1025 miles in 5 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.
How did it go?