Hello, I am reviewing my psat and looking at the questions I got wrong. I can't understand how to do this problem.
Mike and paul left their houses at the same time for a fitness run to the park. Mike ran at an average speed of 7 miles per hour. Paul ran at an average speed of 5 miles per hour. Mike and Paul arrived at the park at the same time. If Mike ran 4 miles farther than Paul, how far, in miles did Mike run?
Mike's time equals Paul's time.
Let D = Paul's distance in miles
Mikes time = (D+4miles)/(7mph)
Paul's time = D/5mph
(D+4miles)/(7mph) = D/(5mph)
Ssolve for D, then find D + 4.
To solve this problem, you need to use the concept of distance equals rate times time, which is commonly known as the distance formula.
Let's call the distance Mike ran as "x" miles and the distance Paul ran as "y" miles. Given that Mike ran 4 miles farther than Paul, we can say that:
x = y + 4
We also know that Mike's average speed is 7 miles per hour and Paul's average speed is 5 miles per hour. Since distance equals rate times time, we can set up two equations using the distances/durations for Mike and Paul:
x = 7t (Mike's distance formula)
y = 5t (Paul's distance formula)
We can use substitution to solve for "x" in terms of "t". Substituting the value of "y" from the equation y = 5t into the equation x = y + 4, we get:
x = 5t + 4
Now, we can equate the two expressions for "x":
7t = 5t + 4
Simplifying this equation, we can subtract 5t from both sides:
7t - 5t = 5t + 4 - 5t
2t = 4
And then divide both sides by 2:
2t/2 = 4/2
t = 2
Now that we know the value of "t" is 2 hours, we can substitute it back into any equation to find the value of "x" or "y". Let's substitute it into Mike's equation:
x = 7t
x = 7(2)
x = 14
Hence, Mike ran a distance of 14 miles.