Damien is a traveling salesperson who needs to drive from Tampa to Melbourne.

However, he does not want to take the Melbourne Expressway (which is a toll road) to save cost so instead he takes the Lake freeway to Orlando and then takes Ocean Freeway to Melbourne.

The direct distance from Tampa to Melbourne is 160 miles, and the distance from Tampa to Orlando is 96 miles.

How much gas will Damien use, assuming his old car gets 7 miles per gallon?

Round to the nearest whole number and then enter numeric values without units and symbols.

Example: If the answer is 89 gallons, enter 89 as your answer.

Question

Damien is a traveling salesperson who needs to drive from Tampa to Melbourne.

However, he does not want to take the Melbourne Expressway (which is a toll road) to save cost so instead he takes the Lake freeway to Orlando and then takes Ocean Freeway to Melbourne.

The direct distance from Tampa to Melbourne is 160 miles, and the distance from Tampa to Orlando is 96 miles.

How much gas will Damien use, assuming his old car gets 7 miles per gallon?

Round to the nearest whole number and then enter numeric values without units and symbols.

Example: If the answer is 89 gallons, enter 89 as your answer.

BlackTom AI · Accepted Answer

The problem describes a triangle of travel distances: Tampa to Orlando is 96 miles, Orlando to Melbourne is along Ocean Freeway, and the direct Tampa to Melbourne distance is 160 miles. The key is to determine the distance Damien travels along the two roads he takes: Tampa → Orlando and Orlando → Melbourne.

First, recognize the relationship given: the direct distance from Tampa to Melbourne is 160 miles, and the distance from Tampa to Orlando is 96 miles. If we suppose Orlando to Melbourne (via Ocean Freeway) is x miles, then the route Damien takes totals 96 + x miles.

Next, use the information that the three cities form a triangle with side lengths 96, x, and 160. The problem’s setup implies a right triangle because 96^2 + x^2 should equal 160^2 if the angle at Orlando is a right angle (this is a common triangle pattern in such problems). Testing with the known distance 160 (the direct Tampa–Melbourne distance) we can solve for x:

96^2 + x^2 = 160^2
9216 + x^2 = 25600
x^2 = 25600 - 9216 = 16384
x = 128 miles

So, the distance Damien travels along the motorways is 96 miles (Tampa to Orlando) plus 128 miles (Orlando to Melbourne) = 224 miles.

Now compute gas usage with the car’s fuel efficiency: 7 miles per gallon. Gas needed = total miles / mpg = 224 / 7 = 32 gallons.

Potential pitfalls to avoid:
- If you try to use only the direct Tampa–Melbourne distance (160 miles), you’d ignore the detour via Orlando and would underestimate gas usage.
- If you misidentify the triangle as obtuse or use an incorrect relationship, you might miscalculate Orlando–Melbourne distance. Checking for a right-triangle relationship here (96, 128, 160) aligns with a 3-4-5 scaling (96:128:160 is proportional to 3:4:5), confirming consistency.
- Roundings: the problem asks for a nearest whole number and a numeric value without units. The calculation yields exactly 32 gallons, so no rounding adjustment is needed.

Therefore, the gas Damien uses is 32 gallons.

ST-MATH-0824-750-49498-202503 Q4 Geometry & Voting

查看解析

登录即可查看完整答案

类似问题

If it takes 30 minutes to mow 1 acre of turf with a ride-on mower, about how long would it take to mow Jesse Owens soccer field? If it takes 2 hours to mow 1 acre of turf with an autonomous mower, about how long would it take to mow Jesse Owens soccer field?

__________________ refers to the products, methods, inventions, and standards used for the purpose of producing information.

____________________ is data presented in a meaningful context.

_________________ framework—a model of the components of an information system: computer hardware, software, data, procedures, and people.

_______________________ is the ability to model the components of the system to connect the inputs and outputs among those components.

___________________ is the ability to make and manipulate models.

_____________ states that the value of a network is equal to the square of the number of users connected to it.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单