Steve made a business trip of 254 miles. He averaged 57 MPH for the first part and 56 MPH for the second part. If the trip took 4.5 hours, how long did he travel at each rate?
If x hours at 57 mi/hr, then since distance = speed * time,
57x + 56(4.5-x) = 254
To find out how long Steve traveled at each rate, we can use a system of equations.
Let's assume Steve traveled at the first rate, 57 MPH, for "x" hours. Therefore, he traveled the remaining time, which is 4.5 - x hours, at the second rate, 56 MPH.
Now, we can set up the equation based on the distance he traveled. The distance traveled at 57 MPH is the product of the rate and time: 57x. Similarly, the distance traveled at 56 MPH is 56(4.5 - x).
Since the total distance traveled is 254 miles, we can set up the equation:
57x + 56(4.5 - x) = 254
Now, let's solve this equation to find the value of "x":
57x + 56(4.5 - x) = 254
57x + 252 - 56x = 254
x + 252 = 254
x = 254 - 252
x = 2
Therefore, Steve traveled at the first rate, 57 MPH, for 2 hours. Substituting this value back into the equation, he traveled at the second rate, 56 MPH, for 4.5 - 2 = 2.5 hours.
So, Steve traveled at a rate of 57 MPH for 2 hours and at a rate of 56 MPH for 2.5 hours.