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?
since time = distance/speed,
12/s - 1 = 12/(s+1)
Hint: 3 is one less than 4.
It takes Connor 4 hours to complete the course?
To solve this problem, we can use the formula: Distance = Rate × Time.
Let's assume Connor's speed is "x" miles per hour. This means Matt's speed would be "(x + 1)" miles per hour because Matt walks 1 mile per hour faster.
The time it takes for Connor to complete the 12-mile course can be calculated as:
Time = Distance / Rate = 12 / x.
Similarly, the time it takes for Matt to complete the 12-mile course is:
Time = Distance / Rate = 12 / (x + 1).
According to the problem, it takes Matt 1 hour less than Connor to complete the course. So, we can write the following equation:
12 / x - 12 / (x + 1) = 1.
To solve this equation, we can multiply both sides by x(x + 1) to get rid of the denominators:
12(x + 1) - 12x = x(x + 1).
Expanding the equation:
12x + 12 - 12x = x^2 + x.
Simplifying the equation:
12 = x^2 + x.
Rearranging the equation:
x^2 + x - 12 = 0.
Now, we can either use factoring or the quadratic formula to solve this equation. Factoring would give us:
(x + 4)(x - 3) = 0.
This means x = -4 or x = 3.
Since time cannot be negative, we can discard the -4 value. Therefore, x = 3.
Now, let's substitute this value back into the equation for Time:
Time = 12 / x = 12 / 3 = 4.
Therefore, it takes Connor 4 hours to complete the 12-mile course.