Answer:
38.6 mi/h
Explanation:
7.4 mi/h = 7.4mi/h * (1/60)hour/min * (1/60) min/s = 0.00206 mi/s
Let v (mi/s) be your original speed, then the time t it takes to go 1 mi/s is
t = 1/v
Since you increase v by 0.00206 mi/s, your time decreases by 15 s, this means
t - 15 = 1/(v+0.00206)
We can substitute t = 1/v to solve for v
[tex]\frac{1}{v} - 15 = \frac{1}{v + 0.00206}[/tex]
We can multiply both sides of the equation with v(v+0.00206)
v+0.00206 - 15v(v+0.00206) = v
[tex]-15v^2 - 0.0308v + 0.00206 = 0[/tex]
[tex]v= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]v= \frac{0.03083\pm \sqrt{(-0.03083)^2 - 4*(-15)*(0.00205)}}{2*(-15)}[/tex]
[tex]v= \frac{0.03083\pm0.35}{-30}[/tex]
v = -0.01278 or v = 0.01 0724 mi/s
Since v can only be positive we will pick v = 0.010724 mi/s or 0.010724*3600 = 38.6 mi/h
