Over a fixed distance speed r varies inversely as time t. If the speed of a car is 30 mph when the time is 6 seconds what would the speed be of the car if the time was 4 seconds
R1/R2 = T2/T1
V1/30 = 4/6
6R1 = 120
R1 = 20
or
R = kT, where k is a constant
given: R = 30 when T = 6
30 = 6k
k = 5
R = 5T
so when t=4
R = 5(4) = 20
To solve this problem, we can use the formula for inverse variation, which states that if two variables (in this case, speed and time) are inversely proportional, their product is constant.
Let's denote the speed as "r" and the time as "t". According to the problem, we have that r * t is constant. We know that the car's speed is 30 mph when the time is 6 seconds, so we can write this as:
(30 mph) * (6 seconds) = k
where k is the constant of variation.
To find the value of k, we solve for it:
180 = k
Now that we know the value of k, we can use it to find the car's speed when the time is 4 seconds. We set up the equation as follows:
r * t = k
r * 4 seconds = 180
Dividing both sides of the equation by 4 seconds gives us:
r = 180 / 4
r = 45 mph
Therefore, if the time was 4 seconds, the speed of the car would be 45 mph.