Connor and Matt walks a 12-mile course as part of a fitness program. Matt walks 1 mi/h faster than Connor, and it takes him 1 hour less than Connor to complete the course. How long does it take Connor to complete the course?
A: It takes Connor 4 hours to complete the course?
correct
To find out how long it takes Connor to complete the course, we can set up a system of equations based on the given information.
Let's say the speed at which Connor walks is x miles per hour. Since Matt walks 1 mi/h faster than Connor, Matt's speed would be (x + 1) miles per hour.
We know that the distance traveled by both of them is 12 miles. We can use the formula Speed = Distance / Time to set up the equations:
For Connor:
Speed = x miles per hour
Distance = 12 miles
Time = Unknown, let's call it t hours
For Matt:
Speed = (x + 1) miles per hour
Distance = 12 miles
Time = t - 1 hours (since it takes him 1 hour less than Connor)
Now we can set up the equations based on the formula:
For Connor:
x = 12 / t
For Matt:
x + 1 = 12 / (t - 1)
Now we have a system of equations:
x = 12 / t
x + 1 = 12 / (t - 1)
We can solve this system of equations to find the value of t, which represents the time it takes Connor to complete the course.
First, let's solve the first equation for x:
x = 12 / t
Now substitute this value of x into the second equation:
(12 / t) + 1 = 12 / (t - 1)
Multiply through by t(t - 1) to eliminate the denominators:
12(t - 1) + t(t - 1) = 12t
Distribute and simplify:
12t - 12 + t^2 - t = 12t
Rearrange the equation:
t^2 - t - 12 = 0
Now we have a quadratic equation. We can factor it or use the quadratic formula to solve for t. Factoring it gives us:
(t - 4)(t + 3) = 0
So, t = 4 or t = -3. Since time cannot be negative, we can conclude that it takes Connor 4 hours to complete the course.
Therefore, the correct answer is: It takes Connor 4 hours to complete the course.