Question

Problem 9

Leon drives a long distance to attend a family reunion. At 12:00 PM, his gas tank is completely filled with
12 gallons of gas. Leon's car uses gas at a constant rate, and after two hours of driving, Leon notices that
his car used five gallons of gas.
Leon will stop to get gas when his tank is one fourth of the way full. If Leon's car continues to use gas at
the same constant rate and Leon makes no other stops on his trip, at what time will Leon stop to get gas?
Be sure to include AM or PM in your answer.

Answer 1

Leon will stop to get gas at 3:36 PM. He uses fuel at a rate of 2.5 gallons per hour and will refuel when his tank is down to one fourth of its capacity, which will be after driving for 3.6 hours starting from 12:00 PM.

Step-by-step explanation:

Leon's car started with 12 gallons of gas and used 5 gallons after two hours, maintaining constant fuel consumption. We need to determine when he will stop for gas, given that he will stop when the gas tank is one fourth full. To do this, we will calculate the rate at which the car uses gas and then find out when the tank reaches one fourth of its capacity.

Calculating the Rate of Fuel Consumption

Leon's car uses 5 gallons in 2 hours which is 5 gallons/2 hours = 2.5 gallons per hour. To find out when Leon will need to stop for gas, we need to determine when his tank will be down to one fourth of its capacity.

Full capacity is 12 gallons, so one fourth would be 12 gallons / 4 = 3 gallons remaining. Since he starts with 12 gallons and needs to stop with 3 gallons left, he will use 12 - 3 = 9 gallons of gas before he stops.

Finding the Time When Leon Will Stop for Gas

To find out how long it takes for Leon to use 9 gallons at a rate of 2.5 gallons per hour, we divide the total gallons by the rate: 9 gallons / 2.5 gallons per hour = 3.6 hours.

Leon started driving at 12:00 PM, so adding 3.6 hours to that time means he will need to stop to refuel at 3:36 PM (since 0.6 of an hour is 36 minutes).

Answer 2

3:36PM

Step-by-step explanation:

Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.

Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at
`(1)/(4)` capacity, we can use the equation:

`(1)/(4) * 12 = \boxed{3}`

This shows
`(1)/(4)` of his tank's capacity (
`12`) is equal to
`3` gallons. This means he will stop for gas when
`3` gallons are remaining.

Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.

`\frac{\mbox{5 gallons}}{\mbox{2 hours}} = \frac{\mbox{2.5 gallons}}{\mbox{1 hours}}`

This is a simple proportion, and now we know he uses
`2.5` gallons of gas per hour.

Now we can how many hours of gas Leon has left.

He has
`7` gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.

`(7-3)/(2.5) = 1.6`

The
`7-3` is because Leon doesn't stop when his tank is empty, he stops
`3` gallons earlier. We are dividing by
`2.5` because that is how much gas he uses per hour, meaning the result of this division (
`1.6`) is how many hours he has left.

Now we can solve for what time Leon will stop to get gas.

12PM +
`2` hours of driving + the remaining
`1.6` hours = 3:36PM

(
`1.6` hours is equal to 1 hour and 36 minutes)

Therefore, Leon will stop for gas at 3:36PM