driving along a crowded freeway you notice that it takes a time to go from one mile marker to the next. when you increase your speed by 8.4 mi/hr the time to go one mile decreased by 14 seconds. What was your original speed?
driving along a crowded freeway you notice that it takes a time to go from one mile marker to the next. when you increase your speed by 8.4 mi/hr the time to go one mile decreased by 14 seconds. What was your original speed?
42.465
To solve this problem, we need to set up an equation based on the given information. Let's use the following variables:
- Let x be your original speed in miles per hour (mi/hr).
- Let t be the original time it takes to travel 1 mile at x mi/hr (in seconds).
We can then set up the equation based on the given information:
\(t' = t - 14\) (Equation 1)
Where \(t'\) is the new time it takes to travel 1 mile after increasing your speed by 8.4 mi/hr.
From the problem statement, we also know that:
\(x + 8.4\) is your new speed in miles per hour.
We can now set up another equation based on the new speed:
\(t' = \frac{1}{x + 8.4}\) (Equation 2)
Now, we can substitute Equation 2 into Equation 1:
\(\frac{1}{x + 8.4} = t - 14\) (Equation 3)
Let's solve Equation 3 for x:
\(\frac{1}{x + 8.4} = t - 14\)
Cross-multiplying:
\(1 = (t - 14)(x + 8.4)\)
Expanding:
\(1 = tx - 14x + 8.4t - 117.6\)
Rearranging:
\(tx - 14x + 8.4t = 118.6\) (Equation 4)
Now, we need another piece of information to solve for x. Perhaps you know either the original time t or the distance between mile markers in miles. Could you provide that information?
if your sped is s, and keeping everything in hours:
1/(s+8.4) = 1/s - 14/3600
s = 42.465 mi/hr