Solve the motion problem. See Examples.EXAMPLE Solving a Motion ProblemTwo cars leave Iowa...

Solve the motion problem. See Examples.

EXAMPLE Solving a Motion Problem

Two cars leave Iowa City, Iowa, at the same time and travel east on Interstate 80. One travels at a constant rate of 55 mph. The other travels at a constant rate of 63 mph. In how many hours will the distance between them be 24 mi?

Step 1 Read the problem. We must find the time it will take for the distance between the cars to be 24 mi.

Step 2 Assign a variable. We are looking for time.

Let t = the number of hours until the distance between them is 24 mi.

The sketch in FIGURE 16 shows what is happening in the problem.

FIGURE 16

To construct a table, we fill in the information given in the problem, using t for the time traveled by each car. We multiply rate by time to get the expressions for distances traveled.

Step 3 Write an equation.

Step 4 Solve.

Step 5 State the answer. It will take the cars 3 hr to be 24 mi apart.

Step 6 Check. After 3 hr, the faster car will have traveled 63 × 3 = 189 mi and the slower car will have traveled 55 × 3 = 165 mi. The difference is

189 − 165 = 24, as required.

EXAMPLE Solving a Motion Problem

Two planes leave Memphis at the same time. One heads south to New Orleans. The other heads north to Chicago. The Chicago plane flies 50 mph faster than the New Orleans plane. In hr, the planes are 275 mi apart. What are their rates?

Step 1 Read the problem carefully.

Step 2 Assign a variable.

Let r = the rate of the slower plane.

Then r + 50 = the rate of the faster plane.

Step 3 Write an equation. As FIGURE 17 shows, the planes are headed in opposite directions. The sum of their distances equals 275 mi.

FIGURE 17

Step 4 Solve.

Step 5 State the answer. The slower plane (headed south) has a rate of 250 mph. The rate of the faster plane is 250 + 50 = 300 mph.

Step 6 Check. Verify that mi.

From a point on a straight road, Marco and Celeste ride bicycles in the same direction. Marco rides at 10 mph and Celeste rides at 12 mph. In how many hours will they be 15 mi apart?