Physics average speed qusetion pls help :)?

Question

Your average speed on the first half of a car trip is 74.0 km/h. How fast do you have to drive on the second half of the trip to achieve an average speed of 85.0 km/h for the whole trip?

can someone pls explain this oen to me?
thankss youuss :)!

Answer 1

distance = (rate)(time)

For the first half of the trip:
x/2 = (74.0 km/h)(t1)
t1 = x/(2 * 74.0 km/h) [1]

For the second half:
x/2 = (v)(t2)
t2 = x/(2v) [2]

For the whole trip:
x = (85.0 km/h)(t1 + t2) [3]

Adding [1] & [2], substitute into [3], and solve for v:
t1 + t2 = x/(2 * 74.0 km/h) + x/(2v)

x = (85.0 km/h)(x/(2 * 74.0 km/h) + x/(2v))
1 = (85.0 km/h)(1/(2 * 74.0 km/h) + 1/(2v))
1/(85.0 km/h) - 1/(2 * 74.0 km/h) = 1/(2v)
(85.0 km/h)(74.0 km/h) / [(2 * 74.0 km/h) - (85.0 km/h)] = v
v = 99.8 km/h