The Learning Activity titled Applying Polyas Four Steps presents the central problem about Speedy Shuttle Solutions at the beginning of the section. How does the given information in the problem answer the specific questions asked in the Step 2 Explanation? If the problem were changed to read …What is the profit from one days operation , what details of the plan would need to change and in what way?
Applying Polya’s Four Steps
Introduction
Consider how you might break up the following problem into the four steps outlined by Polya:
Many shuttles provided by Speedy Shuttle Solutions operate between Reedy airport and downtown Irvington, 25 miles away. One particular shuttle makes 10 round trips per day carrying an average of 21 passengers per trip. The fare each way is $9.00. What are the receipts from one days operation for this particular shuttle?
Step 1: Understand the problem.
Explain in your own words what the question is asking for.
Explanation: The question is essentially asking how much the shuttle company makes in a day (per shuttle), based on the information provided. Often, it is helpful to list out all the essential pieces of information provided:
One-way fare from the airport to Irvington = $9
10 round trips per day
Each trip averages 21 passengers
Distance covered = 25 miles one way (50 miles round trip)
- Step 2: Make a plan for solving it.
- Think about whether you need all the pieces of information given. Do you need to know all the following pieces of information?
- One-way fare from the airport to Irvington = $9
- 10 round trips per day
Each trip = 21 passengers
Distance covered = 25 miles one way/50 miles round trip (non-essential)
Explanation: We do not need to know the distance covered, since the trip price is a flat rate. Also consider these questions:
- How much does one passenger pay to travel from either the airport to Irvington or vice versa?
- How many total passengers does the shuttle carry per day? (Consider both how many trips they make each day and how many passengers are on each trip.)
- Step 3: Carry out the plan.
- Use your critical thinking skills to solve this problem. When you are done, write down your answer.
Explanation: One passenger pays $9 for a one-way trip. Since each trip takes 21 passengers, that is a total of 21 × $9 = $189 per trip. The shuttle makes 10 round trips per day (or 20 one-way trips), so $189 × 20 = $3,780 in receipts per day.
Step 4: Look back on your solution.
- Explanation: Consider whether this answer makes sense in the context of the original problem: 10 round trips = 20 total trips, around 20 passengers, the fare is about $10, so 20 × 20 × $10 = $4,000 (this would be a reasonable estimate for the total receipts for the day). Our solution of $3,780 makes sense!
- -Post adds value by raising novel points or providing new perspectives.
