From city A to city M, located at a distance of 60 km from A, a bus left, and 20 minutes later a passenger car followed it

From city A to city M, located at a distance of 60 km from A, a bus left, and 20 minutes later a passenger car followed it, the speed of which is 40 km / h more than the speed of the bus. Find the speed of a car and a bus if the bus arrived in M city 12 minutes later than the car.

Let x be the speed of the bus.
x + 40 – vehicle speed.
Let’s find the travel time of the bus:
60 / x.
Car travel time:
60 / (x + 40).
The difference in travel time is:
20 + 12 = 32 minutes = 32/60 = 8/15 hours.
Let’s make the equation:
60 / x – 60 / (x + 40) = 8/15.
Reduce by 4.
15 / x – 15 / (x + 40) = 2/15;
225 (x + 40) – 225x – 2x (x + 40) = 0;
9000 – 2x ^ 2 – 80x = 0;
x ^ 2 + 40x – 4500 = 0;
D = 1600 + 18000 = 19600;
x1 = 90 – does not meet the conditions.
x2 = 50 km / h – bus speed.
Let’s find the speed of the car.
50 + 40 = 90 km / h.
Answer: 50 km / h – bus speed, 90 km / h – car speed.