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Mathematical answers to classroom assignments
3. Party A and Party B walk around the city, with Party A walking 8 kilometers per hour and Party B walking 6 kilometers per hour. Now both of them start from the same place at the same time. After B meets A, it will take another 4 hours to return to the original starting point. B How long does it take to go around the city?

Solution: The speed ratio of A and B = 8: 6 = 4: 3.

When they met, B walked 3/7 of the way.

Then 4 hours is 4/7 of the whole trip.

Therefore, the time spent on line B in a week =4/(4/7)=7 hours.

4. Party A and Party B walk from place A to place B at the same time. When Party A completes the whole journey of 1\4, Party B is still 640 meters away from B. When Party A completes the remaining 5\6, Party B completes the whole journey of 7\ 10. What's the distance between AB and place?

Solution: After A left 1/4, the remaining 1- 1/4=3/4.

Then the remaining 5/6 is 3/4×5/6=5/8.

At this time, a * * * left 1/4+5/8=7/8.

Then the distance ratio between Party A and Party B is 7/8: 7/ 10 = 5: 4.

So when A goes 1/4, B goes 1/4×4/5= 1/5.

Then AB distance =640/( 1- 1/5)=800 meters.

When a ship sails between piers A and B, it takes 2 hours to sail along the water from A to B and 3 hours to sail against the water from B to A, so how many hours does it take for a lifebuoy to float from A to B?

Solution: Take the whole distance as a unit 1.

Then the downstream speed = 1/2.

Upstream speed = 1/3

Because downstream speed = ship speed+current speed = ship speed-current speed.

So the water velocity = (downstream velocity-upstream velocity)/2 = (1/2-1/3)/2 =112.

So it takes1(112) =12 hours for the lifebuoy to float from A to B.

134, A, B and C are distributed on the same road from west to east. Party A, Party B and Party C set out from Party A, Party B and Party C at the same time, with Party A, Party B and Party C heading east and Party C heading west; B and C meet at a distance of B 18km, A and C meet at B. When A catches up with B at C, C has passed 32km. So, how many kilometers is the distance between AC?

Solution: Assuming that B and C intersect at point D, this problem can be solved by using proportional knowledge.

① First calculate the length of the CD.

When Party B meets Party C, Party B's CD is 18km.

When A catches up with B, line B CD line C 18+32 = 50km.

Then 18: CD = CD: 50, CD×CD= 18×50=30×30.

So the length of the CD is 30 kilometers.

② Calculate the length of AC again.

C line 50+30 = 80km, A line AC.

The length of line C is 32km, and the BC of line A is 30+ 18=48.

So 32: 48 = 80: AC

Therefore, the length of AC is 80 ÷ 32/48 = 120km.

135, a train passed a 900-meter-long railway bridge, and it took 1 minute and 25 seconds to get on the bridge at the front and leave the bridge at the rear. Then the train passed through a tunnel with a length of 1800 meters at the same speed, and it took 2 minutes and 40 seconds to get the speed of the train and the length of the car body.

2 minutes and 40 seconds = 160 seconds

1 min 25 seconds =85 seconds

Train speed = (1800-900)/(160-85) = 900/75 =12m/s.

Analysis: the two processes are the same, both entering from the front and leaving from the rear, so the distance/multiple use time of the second time is more than the first time = the speed of the train.

body = 12×85-900 = 1020-900 = 120m。

It is relatively easy to ask for a car body.