Time varies inversely as the rate of travel. If Jennifer drove 13 hours at an average rate of 54 miles per hour, how long would thr trip take at a rate of 65 miles per hour

Proportions

Oh right, thanks.

So it would be 13/54 and x/65

No it isn't. It was said that time varies inversely as the rate:

t = k/r
where
t = time (hours)
r = rate (mph)
k = some constant

If we solve for the constant, k,
k = r*t
and this k is the same for all. Therefore if we have two different values for time and rate,
r1 * t1 = r2 * t2
So instead of dividing them (as what you've typed above), we multiply them. Solving,
54 * 13 = 65 * t2

Now just solve for t2. Hope this helps~ `u`

Thanks

To solve this problem, we can use the concept of inverse variation. Inverse variation means that as one variable increases, the other variable decreases at a proportional rate.

Let's denote the time taken for the trip as "t" and the rate of travel as "r". According to the problem, time (t) varies inversely as the rate of travel (r). Mathematically, this can be represented as:

t = k/r

where "k" is a constant of proportionality.

To find the constant of proportionality, we can use the given information. Jennifer drove 13 hours at an average rate of 54 miles per hour. We can substitute these values into the equation:

13 = k/54

To find the value of k, we can solve for it:

k = 13 * 54

k = 702

Now we have the constant of proportionality, k. We can use this value to find the time (t) for a different rate of travel, such as 65 miles per hour. Let's substitute the values into the equation:

t = 702/65

t ≈ 10.8 hours (rounded to one decimal place)

Therefore, the trip would take approximately 10.8 hours at a rate of 65 miles per hour.