Please help me with an average speed word problem? 10 POINTS FOR YOUR TIME!

Having traveled the first 0.25 of the distance of your trip at an average speed of 40.0 km/hr, how fast must you travel for the rest of the trip in order to average 45.0 km/hr?

Please guide me through the steps. I am really at a loss. I am taking online classes so there is no one to teach me :(

You will get your 10 points. I promise.

Average speed is total distance divided by total time.

pick a distance, say 100 km
for the first leg, distance is 25 km, and time is 25 km/40km/h = 0.625 hour
total travel, distance is 100 km, time is 100/45 = 2.222 hour
leg two, distance is 75 km, and time is 2.222–0.625 = 1.597 hr
and speed is 75 / 1.597 = 46.96 km/hour

you will find that if you use a different distance the answer will be the same, or just use D
leg 1 time = (D/4)/40 = D/160
total, time = D/45
leg two, distance is (3/4)D
time is (D/45) – (D/160)
or D(32/1440 – 9/1440) = D(23/1440) = 0.01597D
speed is [ (0.75)D ] / [ 0.01597D ] = 46.96 km/hr

Let's use 400 km as the total distance. t is the time for part 1 of the trip. u is the time for part 2 of the trip. v is the speed you must travel to average 45 km/h

40 * t = 100

t = 2.5

v * u = 300

u = 300 / v


t + u = 2.5 + 300/v = Total time for trip


Average speed * Total time = 400 km
45 (2.5 + 300/v) = 400

112.5 + 13500 / v = 400
13500 / v = 287.5


287.5v = 13500

v = 46.9565 km /h