https://file.aiquickdraw.com/mathbot/file/172625112962460dc4i4i.jpg

The problem describes a scenario where a pizza delivery driver has to make three deliveries and return to the pizza parlor. Here are the details extracted from the image:

- One delivery is 2 miles south and 3.2 miles east of the pizza parlor.
- Another is 2.1 miles due east of the pizza parlor.
- The last delivery is 3 miles south and 1.6 miles west of the pizza parlor.

The streets form a square grid, and the driver can travel at 30 miles per hour. Additionally, each delivery takes 2 minutes to drop off, and we need to find the least amount of time required to make all three deliveries and return to the pizza parlor.

### Let's break the problem into steps:

1. **Coordinates for each delivery**:
   - Delivery 1: (3.2 miles east, 2 miles south)
   - Delivery 2: (2.1 miles east)
   - Delivery 3: (1.6 miles west, 3 miles south)

2. **Driving speed**: 30 miles per hour (which translates to 1 mile every 2 minutes).

3. **Calculation of travel times**: 
   - For each route between the pizza parlor and the delivery locations, compute the time taken based on distance.
   - Include the time taken to drop off the pizzas (2 minutes per delivery).

I will now compute the total distance for an optimal route and the total time required.The total distance for an optimal route is 19.6 miles, and the least amount of time required to complete all three deliveries and return to the pizza parlor is **45.2 minutes**. This includes both travel time and the drop-off time at each delivery location.

Would you like a detailed breakdown of the route, or do you have any further questions?

Here are 5 related questions to consider:
1. How would the time change if the delivery speed was reduced to 25 miles per hour?
2. What if the deliveries were spread out over a circular route rather than a grid?
3. How would adding a fourth delivery point impact the time and distance?
4. Can you calculate the exact route time if each street has varying speed limits?
5. What is the total time if the drop-off time increases to 3 minutes per delivery?

**Tip**: Manhattan distance is helpful when traveling on grid-like city streets because it assumes only horizontal and vertical movement.

You are a pizza delivery driver and find that 3 deliveries are ready to go out. One is 2 miles south and 3.2 miles east of the pizza parlor, another is 2.1 miles due east of the pizza parlor, and the last is 3 miles south and 1.6 miles west of the pizza parlor. The streets form a square grid, with each running either east-west or north-south. Assuming that you can drive an average of 30 miles per hour and each delivery will take 2 minutes to drop off, what is the least amount of time required to make all 3 deliveries and return to the pizza parlor?

Learn how to optimize pizza delivery routes using Manhattan distance and speed-time calculations. This problem involves finding the least time required for 3 deliveries and includes key concepts in distance and optimization. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation