Question

Два велосипедиста выехали из пункта А одновременно в одном направлении. Первый из них ехал со скоростью 7 км/ч, второй – 10 км/ч. Через 30 минут из пункта А в том же направлении выехал третий велосипедист, который догнал первого, а через 1,5 ч. после этого догнал второго. Определить скорость третьего велосипедиста.

Answer 1

Problem Analysis

We have two cyclists who start simultaneously from point A in the same direction. The first cyclist travels at a speed of 7 km/h, and the second cyclist travels at a speed of 10 km/h. After 30 minutes, a third cyclist starts from point A in the same direction and catches up with the first cyclist. Then, 1.5 hours after that, the third cyclist catches up with the second cyclist. We need to determine the speed of the third cyclist.

Solution

Let's assume the speed of the third cyclist is x km/h.

To find the speed of the third cyclist, we can use the formula: speed = distance / time.

# Distance traveled by the first cyclist:

The first cyclist travels for 30 minutes, which is equal to 0.5 hours. Therefore, the distance traveled by the first cyclist is: distance1 = speed1 * time1 = 7 km/h * 0.5 h = 3.5 km.

# Distance traveled by the second cyclist:

The second cyclist also travels for 30 minutes, so the distance traveled by the second cyclist is: distance2 = speed2 * time2 = 10 km/h * 0.5 h = 5 km.

# Distance traveled by the third cyclist:

The third cyclist catches up with the first cyclist after traveling for 1.5 hours. At this point, the first cyclist has already traveled 3.5 km. Therefore, the distance traveled by the third cyclist is: distance3 = distance1 + 3.5 km.

The third cyclist catches up with the second cyclist after traveling for a total of 1.5 hours + 1.5 hours = 3 hours. At this point, the second cyclist has already traveled 5 km. Therefore, the distance traveled by the third cyclist is: distance3 = distance2 + 5 km.

Since both expressions for distance3 are equal, we can set them equal to each other and solve for x:

distance1 + 3.5 km = distance2 + 5 km

Substituting the values of distance1 and distance2:

3.5 km + 3.5 km = 5 km + 5 km

Simplifying the equation:

7 km = 10 km

Since this equation is not true, it means that our assumption for the speed of the third cyclist is incorrect. Let's try a different assumption.

Let's assume the speed of the third cyclist is y km/h.

# Distance traveled by the third cyclist (using the new assumption):

The third cyclist catches up with the first cyclist after traveling for 1.5 hours. At this point, the first cyclist has already traveled 3.5 km. Therefore, the distance traveled by the third cyclist is: distance3 = distance1 + 3.5 km = 3.5 km + 3.5 km = 7 km.

The third cyclist catches up with the second cyclist after traveling for a total of 1.5 hours + 1.5 hours = 3 hours. At this point, the second cyclist has already traveled 5 km. Therefore, the distance traveled by the third cyclist is: distance3 = distance2 + 5 km = 5 km + 5 km = 10 km.

Since both expressions for distance3 are equal, we can set them equal to each other and solve for y:

distance1 + 3.5 km = distance2 + 5 km

Substituting the values of distance1 and distance2:

3.5 km + 3.5 km = 5 km + 5 km

Simplifying the equation:

7 km = 10 km

Again, this equation is not true. It seems that there is no valid solution for the speed of the third cyclist that satisfies the given conditions.

Therefore, we cannot determine the speed of the third cyclist based on the information provided.

Please let me know if there is anything else I can help you with.