The time T required to drive a fixed distance varies inversely as the speed r. it takes five hours at 60 mph to drive a fixed distance. how long would it take to drive the fixed distance at 40 mph?
Thank you so much:)
t = k/r, where k is a constant
given: t = 5, r = 60
5 = k/60
k = 300
t = 300/r
when r = 40
t = 300/40 = 7.5 hrs
To solve this problem, we can use the formula for inverse variation:
T = k / r
where T is the time, r is the speed, and k is the constant of variation.
We are given that it takes 5 hours at 60 mph to drive a fixed distance. Plugging these values into the equation, we get:
5 = k / 60
To find the value of k, we can multiply both sides of the equation by 60:
300 = k
Now that we have the value of k, we can use it to answer the question: How long would it take to drive the fixed distance at 40 mph?
Plugging in the new speed, r = 40, into the formula, we get:
T = 300 / 40
Simplifying, we find:
T = 7.5 hours
Therefore, it would take 7.5 hours to drive the fixed distance at 40 mph.
To solve this problem, we need to use the inverse variation formula:
T = k/r
where T represents the time, r represents the speed, and k is a constant of variation.
Given that it takes 5 hours to drive the fixed distance at 60 mph, we can plug these values into the formula:
5 = k/60
To find the value of k, we can multiply both sides of the equation by 60:
5 * 60 = k
k = 300
Now that we know the value of k, we can use it to find the time required to drive the fixed distance at 40 mph:
T = k/r
T = 300/40
T = 7.5
Therefore, it would take 7.5 hours to drive the fixed distance at 40 mph.