A Mathematical Analysis of Gas Usage in Loaded Pick-Up Truck Trips

What is the expression for the total gas used by a loaded pick-up truck traveling 70 miles and then returning with a 20% better gas mileage for the lighter return trip?

To find the expression for the total gas used by the pick-up truck for the round trip, we need to first calculate the gas used for the initial trip and then for the return trip. For the initial trip of 70 miles, we don't know the gas mileage, so we can assume it to be x. Therefore, the gas used for the first trip would be: Gas used for initial trip = (distance traveled ÷ gas mileage) = 70/x For the return trip, the gas mileage is 20% better than the initial trip. This means that the gas mileage would be 1.2 times the initial gas mileage. Therefore, the gas used for the return trip would be: Gas used for return trip = (distance traveled ÷ gas mileage) = 70/(1.2x) To find the total gas used for the round trip, we simply add the gas used for the initial and return trips: Total gas used = gas used for initial trip + gas used for return trip Total gas used = 70/x + 70/(1.2x) Simplifying the expression by finding the common denominator, we get: Total gas used = (70*1.2x + 70x) / (x*1.2) = (84x) / (1.2x) = 70 Therefore, the expression for the total gas used by the pick-up truck for the round trip is 70.

Understanding the Math behind Gas Usage

Total Gas Usage Formula: The total gas used by a loaded pick-up truck for a round trip can be calculated using the formula: Total Gas Used = Gas Used for Initial Trip + Gas Used for Return Trip Gas Used for Initial Trip: For the initial trip of 70 miles, the gas used can be calculated by dividing the distance traveled by the gas mileage (x) of the pick-up truck. Therefore, Gas Used for Initial Trip = 70/x Gas Used for Return Trip: For the return trip, the gas mileage is 20% better than the initial trip, which means the gas mileage is 1.2 times the initial gas mileage. Therefore, Gas Used for Return Trip = 70/(1.2x) Calculating Total Gas Used: By adding the gas used for the initial and return trips and simplifying the expression, we get Total Gas Used = 70/x + 70/(1.2x) = 70 Therefore, the total gas used by the pick-up truck for the round trip is 70. This simple mathematical analysis helps us understand the relationship between distance traveled, gas mileage, and total gas usage in loaded pick-up truck trips.
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