Pairs of markings a set distance apart are made on highways so that police can detect drivers exceeding the speed limit. Over a fixed distance, the speed R varies inversely with the time T. For one particular pair of markings, R is 60 mph when T is 8 seconds. Find the speed of a care that travels the given distance in 6 seconds.
R = k(1/T) = k/T
when R = 60, T = 8
60 = k/8
k = 480
R = 480/T
so when T = 6
R = 480/6 = 80 mph
Fuartbart
aries inversely with the time T. In one particular pair of markings, R is 45 mph when T is 9 seconds. Find the speed of a car that travels the given distance in 7 seconds
Well, it seems like we've got a need for speed here! Let's put the pedal to the metal and solve this problem.
We know that the speed R varies inversely with the time T. So, we can set up the equation R = k/T, where k is the constant of variation.
Given that R is 60 mph when T is 8 seconds, we can plug these values into the equation: 60 = k/8.
Now it's time for some math magic. We can solve for k by multiplying both sides of the equation by 8: 60 * 8 = k.
So, k = 480.
Now we have the value of k, and we need to find the speed of a car that travels the given distance in 6 seconds. Let's call this speed R2.
Using the equation R = k/T, we can plug in the values we know: R2 = 480/6.
Drumroll, please... calculating... and we find that R2 = 80 mph!
So, the speed of the car that travels the given distance in 6 seconds is 80 mph. Just remember to buckle up and drive safely so you don't become a clown car, zooming around with your funny business!
To solve this problem, we can use the formula for inverse variation:
R = k/T
where R is the speed, T is the time, and k is the constant of variation.
First, let's find the value of k. We are given that when T is 8 seconds, R is 60 mph. Plugging these values into the equation, we have:
60 = k/8
To find k, we can multiply both sides of the equation by 8:
60 * 8 = k
k = 480
Now that we have the value of k, we can use it to find the speed of a car that travels the given distance in 6 seconds. Plugging the values into the equation, we have:
R = 480/6
R = 80 mph
Therefore, the speed of the car that travels the given distance in 6 seconds is 80 mph.