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.

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