### 10.4 Outdoor Sports

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• 7. Average Speed of a Fishing Boat

The 28-foot-long fishing boat has twin turbo diesel engines and a 220-gallon fuel tank. The average cruising speed of the boat to its anchoring point is 20 knots. The horizontal distance between the fishing boat and its anchor is 138 feet. (Note: 1 knot = 1.15 mph).

What is the average speed in miles per hour of the boat to its anchoring point? (See Example 3 and Example 4.)

• Worked-Out Solution

To find the average speed in miles per hour, you must convert from knots to miles per hour.

So, the average speed of the boat is 23 miles per hour.

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``` _    _     _____     _____      ___      _____
| || | ||  |  ___||  |__  //    / _ \\   /  ___||
| || | ||  | ||__      / //    / //\ \\ | // __
| \\_/ ||  | ||__     / //__  |  ___  ||| \\_\ ||
\____//   |_____||  /_____|| |_||  |_|| \____//
`---`    `-----`   `-----`  `-`   `-`   `---`

```
• 8. Finding Distance

The 28-foot-long fishing boat has twin turbo diesel engines and a 220-gallon fuel tank. The average cruising speed of the boat to its anchoring point is 20 knots. The horizontal distance between the fishing boat and its anchor is 138 feet. (Note: 1 knot = 1.15 mph)

The fishing boat takes 48 minutes to cruise straight to its anchoring point from the dock. How far from the dock is the anchoring point? (See Example 3 and Example 4.)

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``` __   __    _____    _    _      ___      _  __
\ \\/ //  |  ___|| | || | ||   / _ \\   | |/ //
\   //   | ||__   | || | ||  | / \ ||  | ' //
/ . \\   | ||__   | \\_/ ||  | \_/ ||  | . \\
/_//\_\\  |_____||  \____//    \___//   |_|\_\\
`-`  --`  `-----`    `---`     `---`    `-` --`

```
• 9. Range of Water Depths

The 28-foot-long fishing boat has twin turbo diesel engines and a 220-gallon fuel tank. The average cruising speed of the boat to its anchoring point is 20 knots. The horizontal distance between the fishing boat and its anchor is 138 feet. (Note: 1 knot = 1.15 mph).

A general rule of thumb is to let out 7 to 10 feet of anchor line for every foot of water depth. The fishing boat in the diagram used this rule when it anchored. What is the range of the depth d of the water? (See Example 3 and Example 4.)

• Worked-Out Solution

From the diagram, you can see that the fishing boat let out 140 feet of anchor line. The lesser the amount of line let out per foot of depth, the deeper the water must be because it would take more of the shorter line to cover the same distance as the longer line. To find the shallowest possible water depth, assume the boat let out 10 feet of line per foot of depth (the greatest amount of line allowed by the rule). Use a conversion factor.

If the water is 14 feet deep, you would only have to let out 10 feet of anchor line 14 times to have 140 feet of line. So, the shallowest possible depth is 14 feet.

To find the deepest possible water depth, assume the boat let out 7 feet of line per foot of depth (the least amount of line allowed by the rule). Use a conversion factor.

If the water is 20 feet deep, you would need to let out 7 feet of line 20 times to have 140 feet of line. So, the deepest possible depth is 20 feet.

So, the range of depths is 14 feet to 20 feet.

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```  _____    __   __  __    __   __   __    ____
|__  //   \ \\/ // \ \\ / //  \ \\/ //  |  _ \\
/ //     \ ` //   \ \/ //    \ ` //   | |_| ||
/ //__     | ||     \  //      | ||    | .  //
/_____||    |_||      \//       |_||    |_|\_\\
`-----`     `-`'       `        `-`'    `-` --`

```
Guest   4 years ago |
I am curious why the answer does not make sense with the pythagorean theorem. According to the pythagorean theorem, the value for d in this diagram would be about 23.6 ft. The answer here is saying the depth is between 14 and 20 feet.
0
• 10. Anchor Chain Length

The 28-foot-long fishing boat has twin turbo diesel engines and a 220-gallon fuel tank. The average cruising speed of the boat to its anchoring point is 20 knots. The horizontal distance between the fishing boat and its anchor is 138 feet. (Note: 1 knot = 1.15 mph)

The anchor line ends with a section of chain. This chain provides extra weight and prevents jagged bottom rocks from cutting the anchor line. The recommended length of an anchor chain is one-half foot for every foot of boat length. What is the recommended length for the boat shown? (See Example 3 and Example 4.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```           __   __    _____    _    _     _____
___    \ \\/ //  |__  //  | || | ||  /  ___||
/   ||   \ ` //     / //   | || | || | // __
| [] ||    | ||     / //__  | \\_/ || | \\_\ ||
\__ ||    |_||    /_____||  \____//   \____//
-|_||    `-`'    `-----`    `---`     `---`
`-`
```
• 11. Maximum Surface Area that an Anchored Boat can Cover

The 28-foot-long fishing boat has twin turbo diesel engines and a 220-gallon fuel tank. The average cruising speed of the boat to its anchoring point is 20 knots. The horizontal distance between the fishing boat and its anchor is 138 feet. (Note: 1 knot = 1.15 mph).

What is the maximum water surface area that the fishing boat can cover when the anchor is stationary? (See Example 3 and Example 4.)

• Worked-Out Solution

The farthest the boat can travel from the anchor is 138 feet plus the length of the boat. The boat is 28 feet long, so the front of the boat can reach a distance of 138 + 28 = 166 feet from the anchor. Because the boundary of the region that the boat can cover is 166 feet from the anchor in any direction, the boat is restricted to traveling inside of a circle with the anchor at the center and a radius of 166 feet. Recall from Section 1.1 that the formula for the area of a circle is

Using , the maximum surface area that the fishing boat can cover when the anchor is stationary is

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```           __   __    _  _     _____     ______
____     \ \\/ //  | \| ||  |  ___||  /_   _//
|    \\    \ ` //   |  ' ||  | ||__      | ||
| [] ||     | ||    | .  ||  | ||__     _| ||
|  __//     |_||    |_|\_||  |_____||  /__//
|_|`-`      `-`'    `-` -`   `-----`   `--`
`-`
```
• 12. Diesel Fuel Weight

The 28-foot-long fishing boat has twin turbo diesel engines and a 220-gallon fuel tank. The average cruising speed of the boat to its anchoring point is 20 knots. The horizontal distance between the fishing boat and its anchor is 138 feet. (Note: 1 knot = 1.15 mph)

Diesel fuel weighs about 7.1 pounds per gallon. How much does three-fourths of a tank of fuel weigh? (See Example 3 and Example 4.)

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  _  __   _    _    _    _      ___    __    __
| |/ // | || | || | || | ||   / _ \\  \ \\ / //
| ' //  | || | || | || | ||  / //\ \\  \ \/ //
| . \\  | \\_/ || | \\_/ || |  ___  ||  \  //
|_|\_\\  \____//   \____//  |_||  |_||   \//
`-` --`   `---`     `---`   `-`   `-`     `

```
• 13. Number of Hours a Fishing Boat can Run on Half a Tank

The 28-foot-long fishing boat has twin turbo diesel engines and a 220-gallon fuel tank. The average cruising speed of the boat to its anchoring point is 20 knots. The horizontal distance between the fishing boat and its anchor is 138 feet. (Note: 1 knot = 1.15 mph)

Diesel engines use about 1 gallon of fuel per hour for every 18 horsepower used. How many hours can the boat run at 342 horsepower on a half tank of fuel? (See Example 3 and Example 4.)

• Worked-Out Solution

The fishing boat has a 220-gallon fuel tank. Because it only has a half tank of fuel, it has

Use a conversion factor to find how many gallons of fuel it takes to run the boat at 342 horsepower for 1 hour.

Divide the number of gallons in the tank by the number of gallons that the boat uses per hour.

So, the fishing boat can run at 342 horsepower on a half tank of gas for about 5.8 hours.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  _  __     ___     _    _      ___     _    _
| |/ //   / _ \\  | || | ||   / _ \\  | \  / ||
| ' //   / //\ \\ | || | ||  / //\ \\ |  \/  ||
| . \\  |  ___  ||| \\_/ || |  ___  ||| .  . ||
|_|\_\\ |_||  |_|| \____//  |_||  |_|||_|\/|_||
`-` --` `-`   `-`   `---`   `-`   `-` `-`  `-`

```
• 14. Fuel Reserves

A general rule of thumb when fishing is to use one-third of the fuel in your tank to get there, use one-third to get back, and save the last third as an emergency backup. The fuel gauge shows the amount of fuel in a fishing boat after reaching its anchor point. Will the boat have enough fuel reserves according to the rule of thumb? Explain your reasoning.

These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.

```  _____     ______    _____      ___       _____
/  ___||  /_   _//  |__  //    / _ \\    / ___//
| // __     -| ||-     / //    | / \ ||   \___ \\
| \\_\ ||   _| ||_    / //__   | \_/ ||   /    //
\____//   /_____//  /_____||   \___//   /____//
`---`    `-----`   `-----`    `---`   `-----`

```