Question 249132: Speed varies inversly with time of travel. It takes 6 seconds to travel between two highway markers at 45 mph. write the equation and show the proportionality constant. How fast are you driving if it takes 5 seconds to travel between the markers?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let t = time
let s = speed
s = k/t
k is the constant of variation.
let t = 6 seconds
let s = 45 miles per hour.
use these values to find k.
equation of s = k/t becomes:
6 seconds = k / 45 miles per hour
without changing the units used, the constant of variation here would be:
k = 6*45 = 270
If it takes 5 seconds, then the equation becomes:
5 = 270 / x and you get
x = 270/5 = 54 miles per hour.
with changing the units used, the equation of:
6 = k/45mph becomes:
6 = k/.0125 miles per second.
now the units are consistent with each other.
solve for k to get:
k = .0125*6 = .075
with 5 seconds, the equation now becomes:
5 = .075 / x
solve for x to get:
x = .075/5 = .015 miles per second.
convert to miles per hour to get 54 miles per hour.
you get the same answer whether you converted the units or not.
the constant of proportionality took care of the difference in the units used.
if you divide the constant of proportionality by 3600 which is what we did to convert the miles per hour to miles per second, then the constant of proportionality of 270 becomes .075.
mathematically the two answers are equivalent to each other.
you did not have to convert the units to make them consistent in this case.
however, in a lot of other cases, you will need to, so converting to similar units for all variables in the equation is always a good idea.
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