Pairs of markings, a set distance apart, are made on highways so that the 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 35mph when T is 6 seconds. Find the speed of a car that travels the given distance in 5 seconds.
R= ___ mph
(round to the nearest whole number.)
inverse variation means that RT = k, a constant.
So, just set up things which are both equal to k:
35*6 = R*5
now just find the R value.
To solve this problem, we can use the inverse variation equation:
R * T = k
where R is the speed, T is the time, and k is the constant of variation. We will use the information given to find the value of k.
Given that R is 35 mph when T is 6 seconds, we can substitute these values into the equation:
35 * 6 = k
Now, we can solve for k:
k = 210
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 5 seconds. We will use the same equation and substitute T = 5:
R * 5 = 210
Now, we can solve for R:
R = 210 / 5
R = 42 mph
Therefore, the speed of the car that travels the given distance in 5 seconds is 42 mph.