A car and a cyclist left one point in opposite directions. After 5/9 hours, the distance between them was 45 km

A car and a cyclist left one point in opposite directions. After 5/9 hours, the distance between them was 45 km. Find car and cyclist speeds if the cyclist’s speed is 35% of the car’s speed.

Let the speed of the car be x km / h and the speed of the cyclist is y km / h. Let’s compose and solve the system of equations:

(x + y) * 5/9 = 45;

x * 35/100 = y;

Substitute the value of y from the second equation into the first equation:

(x + x * 35/100) * 5/9 = 45;

x * (20/20 + 7/20) * 5/9 = 45;

x * 27/20 * 5/9 = 45;

x = 45 * 9/5 * 20/27 = (45 * 9 * 20) / (5 * 27) = 3 * 20 = 60.

y = x * 35/100 = 60 * 35/100 = 21.

Answer: the speed of the car is 60 km / h, and the speed of the cyclist is 21 km / h.