Elaine drives her car 120
miles and has an average of a certain speed. If the average speed had been 7mph
more, she could have traveled 141
miles in the same length of time. What was her average speed?
Let's call Elaine's average speed x mph.
According to the problem, she drives 120 miles at this speed. We can use the formula:
distance = rate x time
to find how long it took her:
120 miles = x mph * time
time = 120 miles / x mph
Now, if her average speed had been 7 mph more, we can set up another equation:
141 miles = (x + 7) mph * time
But we know that time is the same in both equations (since it's the amount of time it took Elaine to drive 120 miles), so we can substitute in our expression for time from the first equation:
141 miles = (x + 7) mph * (120 miles / x mph)
Simplifying this equation:
141 miles = (x + 7) * 120 miles / x
141x = 120x + 840
21x = 840
x = 40
So Elaine's average speed was 40 mph.
Let's assume Elaine's average speed is x mph.
We can set up a equation based on the given information.
Speed * Time = Distance
Using the first scenario where Elaine drives 120 miles:
x * Time = 120 ----(1)
Using the second scenario where the average speed is 7 mph more and she drives 141 miles:
(x + 7) * Time = 141 ----(2)
Now we have a system of equations. We can solve for Time by isolating it in equation (1).
x * Time = 120
Time = 120 / x ----(3)
Substitute this expression for Time in equation (2).
(x + 7) * (120 / x) = 141
Now, let's solve for x.
Multiply both sides by x to eliminate the fraction.
(120 + 7x) = 141x
Move all the x terms to one side and the constant terms to the other.
141x - 7x = 120
134x = 120
Divide both sides by 134 to solve for x.
x = 120 / 134
x ≈ 0.8955
Therefore, Elaine's average speed is approximately 0.8955 mph.