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Example 5.42 from Elementary Algebra, 5.4 Solve Applications with Systems of Equations
Solve Applications with Systems of Equations: example 5.42
Translate to a system of equations and then solve:
Joni left St. Louis on the interstate, driving west towards Denver at a speed of 65 miles per hour. Half an hour later, Kelly left St. Louis on the same route as Joni, driving 78 miles per hour. How long will it take Kelly to catch up to Joni?
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
A diagram is useful in helping us visualize the situation.
Identify and name what we are looking for.
A chart will help us organize the data.
We know the rates of both Joni and Kelly, and so
we enter them in the chart.We are looking for the length of time Kelly,
k, and Joni, j, will each drive.
Since we can fill in the Distance column.Translate into a system of equations.
To make the system of equations, we must recognize that Kelly and Joni will drive the same distance. So,
Also, since Kelly left later, her time will be hour less than Joni’s time.
So,Now we have the system. Solve the system of equations by substitution. Substitute into the second equation, then solve for j. To find Kelly’s time, substitute j = 3 into the first equation, then solve for k. Check the answer in the problem.
Joni 3 hours (65 mph) = 195 miles.
Kelly hours (78 mph) = 195 miles.
Yes, they will have traveled the same distance
when they meet.Answer the question. Kelly will catch up to Joni in hours.
By then, Joni will have traveled 3 hours.
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: Mitchell left Detroit on the interstate driving south towards Orlando at a speed of 60 miles per hour. Clark left Detroit 1 hour later traveling at a speed of 75 miles per hour, following the same route as Mitchell. How long will it take Clark to catch Mitchell?
How did it go?