The car traveled 60 km on the freeway and 32 km on the highway, taking 1 hour for the whole journey.

The car traveled 60 km on the freeway and 32 km on the highway, taking 1 hour for the whole journey. Find the speed of the car on each section of the road if it was moving 20 km / h faster on the highway than on the highway.

To solve this problem, let’s create an equation. Having previously introduced the following designations:
Let the highway speed be x km / h ..
Then the speed of movement on the highway will be (x + 20) km / h ..
According to the condition of the problem, 1 hour was spent on the entire path.
32 / x – driving time on the highway, 60 / (x + 20) – driving time on the highway.
Let’s compose and solve the equation:
32 / x + 60 / (x + 20) = 1;
(32 (x + 20) + 60x) / (x (x + 20)) = 1;
32x + 640 + 60x = x (x + 20);
92x + 640 = x ^ 2 + 20x;
x ^ 2 – 72x – 640 = 0;
D = 72 ^ 2 + 4 * 640 = 7744 = 882;
X1 = (72 + 88) / 2 = 80;
X2 = (72 – 88) / 2 = -8 <0 => value is not valid.
Vehicle speed on the highway, 80 km / h;
The speed of the car on the motorway is then 80 + 20 = 100 km / h;
Answer: 80 km / h; 100 km / h.