Three tanks drove out of the tankport at the same time to the city of Z. The tanks were driving along the same road

Three tanks drove out of the tankport at the same time to the city of Z. The tanks were driving along the same road, the speed of each of them was constant. The speed of the first tank was 40 km / h, the speed of the second tank was 30 km / h. The first tank arrived in the city Z at 13.00, the second tank at 15.00, and the third tank at 17.00. Find the speed of the third tank. Express the answer in km / h.

Given:

v1 = 40 km / h – the speed of the first tank;

v2 = 30 km / h – speed of the second tank;

t1 = 13.00 hours – the time when the first tank arrived in the city;

t2 = 15.00 hours – the time when the second tank arrived in the city;

t3 = 17.00 hours – the time when the third tank arrived in the city.

It is required to determine v3 (km / h) – the speed of the third tank.

According to the terms of the problem, all the tanks left the same point and traveled the same distance.

Let t be the total time of movement of the first tank. Let’s find the difference between the time of entry into the city of the first and second tank:

dt = t2 – t1 = 15 – 13 = 2 hours

Then:

v1 * t = v2 * (t + dt);

v1 * t = v2 * t + v2 * dt;

v1 * t – v2 * t = v2 * dt;

t * (v1 – v2) = v2 * dt;

t = v2 * dt / (v1 – v2) = 30 * 2 / (40 – 30) = 60/10 = 6 hours.

That is, the total distance traveled is:

L = v1 * t = 40 * 6 = 240 kilometers.

The time difference between the first and third tanks is:

dt1 = t3 – t1 = 17 – 13 = 4 hours.

Then the speed of the third tank will be:

v3 = L / (t + dt1) = 240 / (6 + 4) = 240/10 = 24 km / h.

Answer: the speed of the third tank is 24 km / h.