3.5 Solve uniform motion applications  (Page 3/7)

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.

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

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.

$\begin{array}{cccccc}\text{Truck going West}\hfill & & & \text{70 mph (2.5 hours)}\hfill & =\hfill & \text{175 miles}\hfill \\ \text{Truck going East}\hfill & & & \text{60 mph (2.5 hours)}\hfill & =\hfill & \underset{\text{\_\_\_\_\_\_\_\_}}{\text{150 miles}}\hfill \\ & & & & & \text{325 miles}\hfill \end{array}$

$\begin{array}{cccc}\mathbf{\text{Step 7. Answer}}\text{the question with a complete sentence.}\hfill & & & \text{It will take the trucks 2.5 hours to be 325 miles apart.}\hfill \end{array}$