It takes a smaller hose 3 times as long to fill a small swimming pool as it does a larger hose. it takes both hoses working together 30 minutes to fill the swimming pool. how long will it take the smaller hose to fill the pool by itself?

Let the time taken to fill the pool using the larger hose alone be t minutes.
Then the smaller hose used alone will take 3t minutes to fill the pool.
When the hoses are used together for one minute, 1/30 th of the pool volume will be added. Now we can write the following equation:
This simplifies to:

3t = 120
t = 40 minutes.
Therefore the smaller hose will take 3 * 40 = 120 minutes to fill the hose by itself.
The answer is: 120 minutes or 2 hours.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12