Solve Uniform Motion Applications: example 3.50

Two truck drivers leave a rest area on the interstate at the same time. One truck travels east and the other one travels west. The truck traveling west travels at 70 mph and the truck traveling east has an average speed of 60 mph. How long will they travel before they are 325 miles apart?

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.

1
Solution
Step 1. Read the problem. Make sure all the words and ideas are understood.
- Draw a diagram to illustrate what it happening.
- Create a table to organize the information.
Step 2. Identify what we are looking for.
- We are asked to find the amount of time the trucks will travel until they are 325 miles apart.
Step 3. Name what we are looking for. Choose a variable to represent that quantity.
- We are looking for the time travelled. Both trucks will travel the same amount of time. Let’s call the time t. Since their speeds are different, they will travel different distances.
- Complete the chart.
Step 4. Translate into an equation.
- We need to find a relation between the distances in order to write an equation. Looking at the diagram, what is the relationship between the distance each of the trucks will travel?
- The distance traveled by the truck going west plus the distance travelled by the truck going east must add up to 325 miles. So we write:
Step 5. Solve the equation using good algebra techniques.

Now solve this equation. $\begin{matrix} 70 t + 60 t & = & 325 \\ 130 t & = & 325 \\ t & = & 2.5 \end{matrix}$

Table 3.15

So it will take the trucks 2.5 hours to be 325 miles apart.

Step 6. Check the answer in the problem and make sure it makes sense.

Truck going West $\begin{matrix} 70 mph (2.5 hours) & = & 175 miles \end{matrix}$

Truck going East $\begin{matrix} 60 mph (2.5 hours) & = & \underset{________}{150 miles} \\ 325 miles \end{matrix}$

Table 3.16

Step 7. Answer the question with a complete sentence. It will take the trucks 2.5 hours to be 325 miles apart.

Table 3.17

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Pierre and Monique leave their home in Portland at the same time. Pierre drives north on the turnpike at a speed of 75 miles per hour while Monique drives south at a speed of 68 miles per hour. How long will it take them to be 429 miles apart?

How did it go?

Truck going West	$\begin{matrix} 70 mph (2.5 hours) & = & 175 miles \end{matrix}$
Truck going East	$\begin{matrix} 60 mph (2.5 hours) & = & \underset{________}{150 miles} \\ 325 miles \end{matrix}$

Solution

Your turn