Answer:
Steve had an average speed of 62.55 mph while Mary had an average speed of 67.55 mph
Step-by-step explanation:
Here, we want to calculate the average speed of each of the two.
From the question, we are told that Mary drove an average of 5 mph faster than steve.
So, let the average speed of Steve be x mph, this means that the average speed of Mary will be (x + 5) mph
Mathematically;
Time = distance/speed
Time taken by Steve = 845/x hours
Time taken by Mary = 845/(x + 5)
But Mary took an hour less to complete her own trip;
This means that;
if we add one hour to the time spent by Mary, then we will have the time spent by Steve
845/(x + 5) + 1 = 845/x
845/(x + 5) = 845/x -1
845/(x + 5) = (845 - x)/x
Cross multiply;
845(x) = (x + 5)(845-x)
845x = x(845-x) + 5(845-x)
845x = 845x-x^2 + 4225 - 5x
x^2 + 5x - 4225 = 0
We can solve this using the quadratic formula;
x = -b ± √(b^2 - 4ac)/2a
where a = 1 , b = 5 , c = -4225
x = -5 ± √(5^2 - 4(1)(-4225)/2(1)
x = -5 ± √(25 + 16,900)/2
x = -5 ± √(16,925)/2
x = (-5 + 130.1)/2 or (-5-130.1)/2
We ignore the negative side as speed cannot be negative
x = (-5 + 130.1)/2 = 62.548 which is approximately 62.55 mph
So steve’s speed is 62.55 mph while Mary’s speed = 62.55 + 5 = 67.55 mph
