The time it takes to complete a given trip varies inversely as the speed traveled. If it takes Tim 10 hours tro travel from Cleveland to Albany at 42 mi/h, how long will it take him to make the trip at 60 mi/h?
t = k/v^2
so, tv^2 is constant. Therefore,
10/42^2 = t/60^2
oops.
10*42^2 = t*60^2
To solve this problem, we need to understand the concept of inverse variation. Inverse variation means that as one variable increases, the other variable decreases, and vice versa. In this case, the time it takes to complete a trip is inversely proportional to the speed traveled.
We can use the formula for inverse variation:
y = k/x
where y is the first variable (time), x is the second variable (speed), and k is the constant of variation.
In the problem, we are given that it takes Tim 10 hours to travel from Cleveland to Albany at a speed of 42 mi/h. Using this information, we can solve for k:
10 = k/42
To find k, we can cross multiply:
10 * 42 = k
k = 420
Now that we have the constant of variation (k), we can use it to solve the second part of the problem. We need to find the time it will take Tim to make the trip at a speed of 60 mi/h.
Using the formula for inverse variation again, we can set up the equation:
y = k/x
Let's call the time it takes to make the trip at a speed of 60 mi/h as t:
t = 420/60
t = 7 hours
Therefore, it will take Tim 7 hours to make the trip from Cleveland to Albany at a speed of 60 mi/h.