If a cyclist increases his speed by 3 miles per hour, he can reduce the time required for a 6 mile trip by 10 minutes. What is the slower speed?

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.