Respuesta :
Answer:
Slower speed = 9 mph
Step-by-step explanation:
Let the initial speed (slower speed) = s mph
Speed 's' = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
s = [tex]\frac{6}{t}[/tex] -------(1)
If the cyclist increases the speed by 3 mph then the final speed = (s + 3) mph
He can reduce the time 't' by 10 minutes ([tex]\frac{1}{6}[/tex] hours)
Now, (s + 3) = [tex]\frac{6}{t-\frac{1}{6}}[/tex]
s + 3 = [tex]\frac{36}{6t-1}[/tex] --------(2)
Substitute the value of 's' from equation (1) to the equation (2).
[tex]\frac{6}{t}+3=\frac{36}{6t-1}[/tex]
[tex]\frac{2}{t}+1=\frac{12}{6t-1}[/tex]
[tex]\frac{2}{t}-\frac{12}{6t-1}=-1[/tex]
[tex]\frac{2(6t-1)-12t}{t(6t-1)}=-1[/tex]
[tex]\frac{12t-2-12t}{t(6t-1)}=-1[/tex]
[tex]-\frac{2}{t(6t-1)}=-1[/tex]
6t² - t = 2
6t² - t - 2 = 0
6t² - 4t + 3t - 2 = 0
2t(3t - 2) + 1(3t - 2) = 0
(2t + 1)(3t - 2) = 0
t = [tex]-\frac{1}{2},\frac{2}{3}[/tex] hours
But the time can't be negative.
Therefore, t = [tex]\frac{2}{3}[/tex] hours is the answer.
From equation (1),
s = [tex]\frac{6}{\frac{2}{3}}[/tex]
s = 9 miles per hour.
Slower speed = 9 mph is the answer.
