Two cars left points M and N at the same time towards each other. One of them arrived at N 1 hour 15

Two cars left points M and N at the same time towards each other. One of them arrived at N 1 hour 15 minutes after the meeting, and the other at M 48 minutes after the meeting. The distance between points M and N is 90 km. Find vehicle speeds.

1 h 15 min = 1.25 h
48 minutes = 0.8 hours
The speed of the first is x km / h, the second is y km / h. The first after the meeting drove 1.25X km, the second 0.8Y km.
The first one spent 90 / X hours for the whole journey, the second 90 / X hours. Before the meeting, both were on the road at the same time. This means that the first one spent 1.25-0.8 = 0.45 hours more for the entire journey from M to N, or 90 / X – 90 / Y = 0.45
Let’s compose and solve the system:
1.25X + 0.8Y = 90; X = 72 – 0.64U;
90 / X – 90 / Y = 0.45; 90 / (72 – 0.64Y) – 90 / Y = 0.45;
90 / (72 – 0.64U) – 90 / Y = 0.45;
(90Y – 6480 + 57.6Y) / (72Y – 0.64Y ^ 2) = 0.45;
147.6Y – 6480 = 32.4Y – 0.288Y ^ 2;
Y ^ 2 + 400Y – 22500 = 0;
Y1 = 50;
Y2 = -450 – does not meet the conditions of the problem.
X = 40; Y = 50.
Answer: the speed of the first is 40 km / h; the speed of the second is 50 km / h.