Solution:
Suppose a needs x hours, then b needs x- 1 hour, and a actually needs x-3 hours.
Because the distance is the same, so:
40*(X-3)=35*(X- 1)
X= 17。
So the distance =( 17-3)*40=560 kilometers.
2. The east and west villages are 20 kilometers apart. After 4 kilometers from the East Village to the West Village, Party B will catch up with Party A at a speed of 6 kilometers per hour, and immediately return to the East Village at the original speed after catching up. When Party B arrived in the East Village, Party A just arrived in the West Village. What is the speed of asking A?
Solution: First calculate the round-trip time of B: 20x2÷6=20/3 (hours).
That is to say, A ran the distance of 20-4= 16 (km) in 20/3 hours (because A set off from East Village to West Village for 4 km before B set off).
So the speed of A is (20-4)÷20/3=48÷20=2.4 (km/h).
3. On the 300-meter-long circular track, Party A and Party B run in the same place and direction at the same time, with Party A running 5 meters per second and Party B running 4.4 meters per second. What is the first meeting point between them after departure?
Solution: Let the first meeting be 5x-4.4x = 300 x = 500 seconds, 500 * 5 = 2500m2500/300 = 8-100m, and meet at a distance of100m.
4. The tortoise and rabbit started at the same time, with a total distance of 7000m. The tortoise crawls at a speed of 30 meters per minute, and the rabbit runs at a speed of 330 meters per minute. After running 10 minutes, the rabbit stopped to sleep for 200 minutes, and immediately ran forward at the same speed after waking up. When the rabbit catches up with the tortoise, how many kilometers is it from the finish line?
Solution: The rabbit ran for 10 minutes, then stopped to sleep for 200 minutes. Then the tortoise ran 30× 265,438+00 = 6300m, and the rabbit only ran 3300m. The pursuit distance is 6300-3300 = 3000 meters. Divide the chasing distance by the speed difference between the two, 3000/(330 tortoise * * * runs 200+ 10+ 10 = 220 minutes, and the speed of riding the tortoise is 220× 30 = 6600 meters, so there is still 400 meters from the finish line.
5. There is a male and a female athlete practicing long-distance running on the circular track. The running speed is constant, and the male athlete runs a little faster than the female athlete. If they start from the same starting point and run in the opposite direction at the same time, they will meet every 25 seconds. Now, they start from the same starting point and run in the same direction at the same time. 13 minutes later, the male athlete caught up with the female athlete. How many laps did the female athlete run when she caught up? (The number of laps is rounded off)
[Title] Question 6 in the Final of the 6th Mathematical Contest of Decimal Newspaper.
Answer: 15 cycles