Answer:
Slower speed = 9 mph
Step-by-step explanation:
Let the initial speed (slower speed) = s mph
Speed 's' =
s = -------(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 ( hours)
Now, (s + 3) =
s + 3 = --------(2)
Substitute the value of 's' from equation (1) to the equation (2).
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 = hours
But the time can't be negative.
Therefore, t = hours is the answer.
From equation (1),
s =
s = 9 miles per hour.
Slower speed = 9 mph is the answer.