Micah walks on a treadmill at 4 miles per hour. He has walked 2 miles when Luke starts running at 6 miles per hour on the treadmill next to him. If their rates continue, will Luke's distance ever equal Micah's distance? Explain.
*At 5 hours Luke will run 30 miles and at 8 hours Micah will run 30 miles.
Is this correct?
oh my gosh my answer was so silly,
thanks.
No, that is not correct. Let me explain the situation step-by-step:
1. Micah walks on a treadmill at a speed of 4 miles per hour.
2. Micah has already walked 2 miles.
Now, let's calculate the distance covered by Luke based on his speed:
3. Luke runs on the treadmill at a speed of 6 miles per hour.
To determine if Luke's distance will ever equal Micah's distance, we can compare the rates at which they are covering distance:
4. Micah walks at a rate of 4 miles per hour.
5. Luke runs at a rate of 6 miles per hour.
Since Luke's speed (6 miles per hour) is greater than Micah's speed (4 miles per hour), Luke's distance will always be greater than Micah's distance.
Therefore, Luke's distance will eventually surpass and continue to be greater than Micah's distance as long as they both continue at their respective speeds.
No, the statement that at 5 hours Luke will run 30 miles and at 8 hours Micah will run 30 miles is not correct.
To determine if Luke's distance will ever equal Micah's distance, we need to compare their rates of movement and the distance Micah has already walked.
Micah walks on a treadmill at a rate of 4 miles per hour. So after t hours, Micah will have walked a distance of 4t miles.
Luke starts running at a rate of 6 miles per hour, but he starts when Micah has already walked 2 miles. So after t hours, Luke will have run a distance of 6t - 2 miles.
To find out if Luke's distance will ever equal Micah's distance, we need to set up an equation:
4t = 6t - 2
Simplifying this equation, we get:
2t = 2
Dividing both sides by 2, we find:
t = 1
So after 1 hour, Luke will have run a distance of 6(1) - 2 = 4 miles. In that same hour, Micah will have walked a distance of 4(1) = 4 miles.
Therefore, after 1 hour, Luke's distance will equal Micah's distance. So the answer to the question is yes, Luke's distance will eventually equal Micah's distance.
After t more hours:
Micah has walked 2 + 4t miles
Luke ran 6t miles
6t = 4t + 2
2t=2
t = 1
So after one hour, they will have gone the same distance, each one has gone 6 miles.