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Carina is driving from her home in Anaheim to Berkeley on the same day her brother is driving from Berkeley to Anaheim, so they decide to meet for lunch along the way in Buttonwillow. The distance from Anaheim to Berkeley is 410 miles. It takes Carina 3 hours to get to Buttonwillow, while her brother drives 4 hours to get there. The average speed Carina’s brother drove was 15 miles per hour faster than Carina’s average speed. Find Carina’s and her brother’s average speeds.
Carina 50 mph, brother 65 mph
Ashley goes to college in Minneapolis, 234 miles from her home in Sioux Falls. She wants her parents to bring her more winter clothes, so they decide to meet at a restaurant on the road between Minneapolis and Sioux Falls. Ashley and her parents both drove 2 hours to the restaurant. Ashley’s average speed was seven miles per hour faster than her parents’ average speed. Find Ashley’s and her parents’ average speed.
parents 55 mph, Ashley 62 mph
As you read the next example, think about the relationship of the distances traveled. Which of the previous two examples is more similar to this situation?
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?
Step 1. Read the problem. Make sure all the words and ideas are understood.
Step 2. Identify what we are looking for.
Step 3. Name what we are looking for. Choose a variable to represent that quantity.
Step 4. Translate into an equation.
Step 5. Solve the equation using good algebra techniques.
$\phantom{\rule{2.7em}{0ex}}\begin{array}{cccccc}\text{Now solve this equation.}\hfill & & & \hfill 70t+60t& =\hfill & 325\hfill \\ & & & \hfill 130t& =\hfill & 325\hfill \\ & & & \hfill t& =\hfill & 2.5\hfill \end{array}$
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.
$\begin{array}{cccccc}\text{Truck going West}\hfill & & & \text{70 mph (2.5 hours)}\hfill & =\hfill & \text{175 miles}\hfill \\ \text{Truck going East}\hfill & & & \text{60 mph (2.5 hours)}\hfill & =\hfill & \underset{\text{\_\_\_\_\_\_\_\_}}{\text{150 miles}}\hfill \\ & & & & & \text{325 miles}\hfill \end{array}$
$\begin{array}{cccc}\mathbf{\text{Step 7. Answer}}\phantom{\rule{0.2em}{0ex}}\text{the question with a complete sentence.}\hfill & & & \text{It will take the trucks 2.5 hours to be 325 miles apart.}\hfill \end{array}$
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?
3 hours
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