https://file.aiquickdraw.com/mathbot/file/1727014355289ivdpxm6j.jpg

Let's solve the two problems shown in the image.

### Problem 7:
**The ratio of the speed of a boat to the stream is 7:2. The boat takes 6 hours more traveling upstream than downstream. What is the time taken by the boat for the entire journey?**

Let:
- \( b \) = speed of the boat in still water
- \( s \) = speed of the stream
- The ratio of boat to stream speeds is given as \( 7:2 \), so we can write:
  \[
  \frac{b}{s} = \frac{7}{2} \quad \text{or} \quad b = \frac{7}{2}s
  \]
- Let \( D \) be the total distance traveled both upstream and downstream.

**Upstream speed** = \( b - s \)  
**Downstream speed** = \( b + s \)

Given that the boat takes 6 hours more to travel upstream, the time difference equation is:
\[
\frac{D}{b - s} - \frac{D}{b + s} = 6
\]
Substituting \( b = \frac{7}{2}s \) into the equation:
\[
\frac{D}{\frac{7}{2}s - s} - \frac{D}{\frac{7}{2}s + s} = 6
\]
This can be solved to find \( D \), and once \( D \) is known, we can calculate the time for the entire journey (upstream and downstream).

### Problem 8:
**The angles of a quadrilateral are in the ratio 7:17:19:29. What is the measure of the angles?**

The sum of the angles in any quadrilateral is \( 360^\circ \). Let the angles be \( 7x, 17x, 19x, 29x \).

Thus, the equation becomes:
\[
7x + 17x + 19x + 29x = 360
\]
Simplifying:
\[
72x = 360
\]
\[
x = 5
\]
Therefore, the angles are:
\[
7x = 35^\circ, \quad 17x = 85^\circ, \quad 19x = 95^\circ, \quad 29x = 145^\circ
\]

Let me know if you'd like more details or clarification on these solutions!

### Related Questions:
1. How would the time change if the boat and stream speed ratio was different?
2. How does the distance factor into the time calculations for upstream and downstream journeys?
3. Can you calculate the individual upstream and downstream times once you know the total time?
4. What is the general formula for the sum of angles in any polygon?
5. Can we determine the side lengths of a quadrilateral given just the angles?

### Tip:
In problems with speed and time, always focus on the relationship between speed, time, and distance: \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).

1. The ratio of the speed of a boat to the stream is 7:2. The boat takes 6 hours more traveling upstream than downstream. What is the time taken by the boat for the entire journey?
2. The angles of a quadrilateral are in the ratio 7:17:19:29. What is the measure of the angles?

Learn how to solve two math problems involving a boat's speed in relation to the stream (upstream and downstream) and a quadrilateral's angles in a ratio of 7:17:19:29. This exercise covers ratio, algebra, and geometric properties for Grades 9-10.

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