On jiamin's trip to wisconsin, her average rate of speed for the whole 5-hour trip was 62 miles per hour. for the first two hours of her trip, she kept her average speed at 60 miles per hour. then she realized she was going to be late, so she started driving faster. what was her average speed for the last three hours of her trip?

Average speed for the entire journey was 62 miles per hour.
Total time of the journey was 5 hours.

In first 2 hours, her average speed was 60 miles per hour. This means, she covered 120 miles in first two hours, as

Distance = Speed x Time

The total distance of the entire journey was:

Total Distance = 62 x 5 =310 miles

Out of these 310 miles, she covered 120 miles in first two hours. So this means she covered (310 - 120) miles in next 3 hours.

Thus she covered 190 miles in 3 hours. So her average speed will be 190/3 miles per hour which is equal to 63.33 miles per hour.

So, the average speed for last 3 hours of the trip was 63.33 miles per hour

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