### Problem StatementA cruise boat travels 12 miles downstream in 2 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream.### Options- **A.** 4.002 mph- **B.** 6 mph- **C.** 1.998 mph- **D.** 10.002 mph### ExplanationGiven:- Downstream distance: 12 miles- Downstream time: 2 hours- Upstream time: 6 hours We can calculate the speeds as follows:1. **Downstream speed calculation:** \[ \text{Downstream speed} = \frac{\text{Distance downstream}}{\text{Downstream time}} \] \[ \text{Downstream speed} = \frac{12 \text{ miles}}{2 \text{ hours}} = 6 \text{ mph} \]2. **Upstream speed calculation:** \[ \text{Upstream speed} = \frac{\text{Distance upstream}}{\text{Upstream time}} \] \[ \text{Upstream speed} = \frac{12 \text{ miles}}{6 \text{ hours}} = 2 \text{ mph} \]3. **Boat speed and stream speed:** - Let $ V_b $ be the speed of the boat in still water. - Let $ V_s $ be the speed of the stream. For downstream, $ V_b + V_s = 6 \text{ mph} $ For upstream, $ V_b - V_s = 2 \text{ mph} $ Solving these two equations, we get: \[ V_b + V_s = 6 \] \[ V_b - V_s = 2 \] Adding the two equations: \[ 2V_b = 8 \implies V_b = 4 \text{ mph} \] Substituting $ V_b = 4 \text{ mph} $ into $ V_b + V_s = 6 $: \[ 4 + V_s = 6 \implies V_s = 2 \text{ mph} \]**Conclusion:**- The speed of

closest option to the answer is C

Answered: A cruise boat travels 12 miles…

A cruise boat travels 12 miles downstream in 2 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream. OA. 4.002 mph OB. 6 mph O C. 1.998 mph OD. 10.002 mph

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Problem Statement

A cruise boat travels 12 miles downstream in 2 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream.

### Options
- **A.** 4.002 mph
- **B.** 6 mph
- **C.** 1.998 mph
- **D.** 10.002 mph

### Explanation

Given:
- Downstream distance: 12 miles
- Downstream time: 2 hours
- Upstream time: 6 hours

We can calculate the speeds as follows:

1. **Downstream speed calculation:**
\[
\text{Downstream speed} = \frac{\text{Distance downstream}}{\text{Downstream time}}
\]
\[
\text{Downstream speed} = \frac{12 \text{ miles}}{2 \text{ hours}} = 6 \text{ mph}
\]

2. **Upstream speed calculation:**
\[
\text{Upstream speed} = \frac{\text{Distance upstream}}{\text{Upstream time}}
\]
\[
\text{Upstream speed} = \frac{12 \text{ miles}}{6 \text{ hours}} = 2 \text{ mph}
\]

3. **Boat speed and stream speed:**
- Let $ V_b $ be the speed of the boat in still water.
- Let $ V_s $ be the speed of the stream.

For downstream, $ V_b + V_s = 6 \text{ mph} $

For upstream, $ V_b - V_s = 2 \text{ mph} $

Solving these two equations, we get:
\[
V_b + V_s = 6
\]
\[
V_b - V_s = 2
\]

Adding the two equations:
\[
2V_b = 8 \implies V_b = 4 \text{ mph}
\]

Substituting $ V_b = 4 \text{ mph} $ into $ V_b + V_s = 6 $:
\[
4 + V_s = 6 \implies V_s = 2 \text{ mph}
\]

**Conclusion:**
- The speed of

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