The beach is a favorite destination for most people during the summer.
A) If the closest beach is 365 miles away bow long will it take to reach the beach if you travel at a speed of 62 mph?
B) If your car gets 15.1 miles/gal and gas costs $2.75/gal, what does it cost to travel 365 miles!
The correct answer and explanation is :
Let’s break down both parts of this problem step by step:
Part A: Time to Travel to the Beach
To calculate how long it will take to reach the beach, we need to use the formula for time:
[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
]
Where:
- Distance = 365 miles
- Speed = 62 mph
Substituting the given values:
[
\text{Time} = \frac{365 \text{ miles}}{62 \text{ mph}} = 5.88 \text{ hours}
]
So, it will take approximately 5.88 hours to reach the beach.
Part B: Cost of Gas for the Trip
To calculate the cost of gas for the trip, we need to determine how many gallons of gas will be used and then multiply by the cost per gallon.
- Determine the number of gallons needed:
- We know the car gets 15.1 miles per gallon (mpg), so we can calculate the number of gallons used by dividing the total distance by the miles per gallon:
[
\text{Gallons required} = \frac{\text{Distance}}{\text{Miles per gallon}} = \frac{365 \text{ miles}}{15.1 \text{ mpg}} = 24.2 \text{ gallons}
]
- Calculate the cost of gas:
- The cost of gas is $2.75 per gallon. So, to find the total cost of gas for the trip, we multiply the number of gallons by the price per gallon:
[
\text{Cost} = 24.2 \text{ gallons} \times 2.75 \text{ dollars/gallon} = 66.55 \text{ dollars}
]
So, it will cost $66.55 for the gas needed to travel 365 miles.
Explanation:
For Part A, we used the formula for time, which is a simple application of dividing the distance traveled by the speed at which you’re traveling. The time it takes to travel a given distance at a constant speed is directly proportional to the distance and inversely proportional to the speed.
For Part B, we first determined how many gallons of gas the car would consume by dividing the total distance by the car’s fuel efficiency (miles per gallon). Once we knew how many gallons would be needed, we multiplied that by the cost per gallon of gas to get the total cost of the fuel.
In everyday life, understanding how to calculate both the time and cost of a trip is useful for planning long-distance travels, budgeting for expenses, and optimizing routes for fuel efficiency.