Beth's car has a gas tank that can hold 15 gallons of gas. Her car uses
1/30 of a gallon of gas per mile driven.
Darcy's car has a gas tank that can hold 16 gallons of gas. His car uses
1/25 of a gallon of gas per mile driven.
Both cars start with full tanks of gas. After how many miles will both cars have the same number of gallons of gas remaining in their gas tanks?
x = miles
gas remaining in Beth tank = 15 - x/30
gas remaining in Darcy tank = 16 - x/25
so
15 - x/30 = 16 - x/25
or
1 = x (1/25 - 1/30)
1 = x (.0066666666.....
x = 150 miles
I still really need to know the math to this problem. I don't get how to do it at all! HELP ME PLEASE! D:
To find out after how many miles both cars will have the same number of gallons of gas remaining in their tanks, we can set up an equation based on their fuel consumption rates.
Let's assume that after x miles, both cars will have the same number of gallons of gas remaining.
For Beth's car:
Remaining gas in Beth's car = 15 - (1/30) * x
For Darcy's car:
Remaining gas in Darcy's car = 16 - (1/25) * x
Setting both equations equal to each other:
15 - (1/30) * x = 16 - (1/25) * x
Now, we can solve this equation to find the value of x:
Multiply through by 150 (to get rid of the denominators):
150 * (15 - (1/30) * x) = 150 * (16 - (1/25) * x)
2250 - 5x = 2400 - 6x
Rearrange the equation by adding 6x and subtracting 2250 from both sides:
6x - 5x = 2400 - 2250
x = 150
Therefore, after 150 miles, both cars will have the same number of gallons of gas remaining in their tanks.
To solve this problem, we need to set up and solve the equation for each car to find the point at which they have the same number of gallons of gas remaining.
Let's start with Beth's car.
Beth's car uses 1/30 of a gallon of gas per mile driven. Let's say she has x miles remaining before her tank is empty. Since she started with a full tank of 15 gallons, she will have 15 - (1/30)x gallons of gas remaining.
Now let's move on to Darcy's car.
Darcy's car uses 1/25 of a gallon of gas per mile driven. If he has y miles remaining before his tank is empty, he will have 16 - (1/25)y gallons of gas remaining, as he started with a full tank of 16 gallons.
To find the point where both cars have the same number of gallons remaining, we need to set up an equation and solve for x and y.
We know that the number of gallons remaining is the same for both cars. So, we can set up the equation:
15 - (1/30)x = 16 - (1/25)y
To get rid of the fractions, we can multiply through by the common denominator, which is 750:
750(15 - (1/30)x) = 750(16 - (1/25)y)
Expanding the equation:
11250 - 25x = 12000 - 30y
Now, we can solve this equation to find the values of x and y at which both cars have the same number of gallons remaining.
Let's simplify the equation:
25x - 30y = -750
Now, let's solve for x in terms of y:
25x = 30y - 750
x = (30y - 750)/25
x = (6y - 150)/5
Now we can substitute this expression for x into the equation we set up earlier:
15 - (1/30)((6y - 150)/5) = 16 - (1/25)y
Multiplying through by 30 to get rid of the fractions:
450 - 6(6y - 150) = 480 - (30/25)y
Expanding and simplifying:
450 - 36y + 900 = 480 - (6/5)y
Combining like terms:
-36y + 1350 = -6y + 480
Now, let's solve for y:
-36y + 6y = 480 - 1350
-30y = -870
y = 29
Now that we have the value of y, we can substitute it back into the expression for x:
x = (6y - 150)/5
x = (6(29) - 150)/5
x = (174 - 150)/5
x = 24/5
x = 4.8
So, after approximately 4.8 miles, both cars will have the same number of gallons of gas remaining in their tanks.