Formula of mathematical water flow problem
Navigation problem formula
(1) General formula: still water speed (ship speed)+current speed (water speed) = downstream speed; Ship speed-water speed = water flow speed; (downstream speed+upstream speed)? 2= ship speed; (downstream speed-upstream speed)? 2= water velocity
(2) The formula for two ships sailing in opposite directions: downstream speed of ship A+upstream speed of ship B = still water speed of ship A+still water speed of ship B..
(3) Formula for two ships sailing in the same direction:
Hydrostatic speed of rear (front) ship-Hydrostatic speed of front (rear) ship = the speed of narrowing (expanding) the distance between two ships.
For example, it takes the same time for a ship to sail 80 kilometers downstream as it does for a ship to sail 60 kilometers upstream. Given that the current speed is 3km/h, find the ship speed in still water.
Ship speed in current = ship speed in still water+ship speed in current = ship speed in still water-water speed.
Formula of running water problem
1. Bon voyage = (ship speed+water speed)? Shunshui time
2. Downstream speed = ship speed+current speed.
3. Upstream stroke = (ship speed-water speed)? Backward time
4. Current speed = ship speed-current speed still water
Still water speed (ship speed) = (downstream speed+countercurrent speed)? 2
Water velocity = (downstream velocity-upstream velocity)? 2
Examples of Mathematical Flow Problems
1. The distance between the two docks is 352 kilometers. It takes 1 1 hour for the ship to travel downstream, and 16 hour for the ship to travel upstream. Find the current velocity of the river.
2. The waterway between Port A and Port B is 208km long. A ship sails from port A to port B, arrives at the port in 8 hours, returns to port A from port B, and reaches against the current 13 hours. Find the speed of the ship in still water (ship speed) and water speed.
The distance between the two docks is 240 kilometers. It takes six hours for motorboats to travel along the river, and the current speed of this river is 8 kilometers per hour. How many hours does it take for this motorboat to travel against the current?
The waterway between terminal A and terminal B is 80km long. It takes 4 hours for ship A to go downstream, and it takes 10 hour for ship B to go upstream. If it takes five hours for ship B to go downstream, what is the speed of ship B in still water?
5. It takes 18 hours for A ship to sail 360 kilometers upstream, 15 hours for returning to the original place, and 15 hours for B ship to sail the same distance upstream. How many hours does it take to get back to the original place?
6. In still water, the speed of ship A and ship B is 26 km/h and 22 km/h respectively. The two ships set sail from Ping 'an Port, and B set sail two hours earlier than A. If the current speed is 6 kilometers per hour, how many hours after A sets sail, can it catch up with B?
1. The distance between the two docks is 352 kilometers. It takes 1 1 hour for the ship to travel downstream, and 16 hour for the ship to travel upstream. Find the current velocity of the river.
(352? 1 1-352? 16)? 2=5 km/h
2. The waterway between Port A and Port B is 208km long. A ship sails from port A to port B, arrives at the port in 8 hours, returns to port A from port B, and reaches against the current 13 hours. Find the speed of the ship in still water (ship speed) and water speed.
(208? 8+208? 13)? 2=2 1 km/hour ship speed
(208? 8-208? 13)? 2 = water flow speed of 5 km/h
The distance between the two docks is 240 kilometers. It takes six hours for motorboats to travel along the river, and the current speed of this river is 8 kilometers per hour. How many hours does it take for this motorboat to travel against the current?
240? (240? 6-8-8)= 10 hour
The waterway between terminal A and terminal B is 80km long. It takes 4 hours for ship A to go downstream, and it takes 10 hour for ship B to go upstream. If it takes five hours for ship B to go downstream, what is the speed of ship B in still water?
(80? 4-80? 10)? 2=6 km/h water flow speed
80? 5-6= 10 km/h ship speed
5. It takes 18 hours for A ship to sail 360 kilometers upstream, 15 hours for returning to the original place, and 15 hours for B ship to sail the same distance upstream. How many hours does it take to get back to the original place?
(360? 10-360? 18)? 2=8 km/h water flow speed
360? 15+8+8 = 40km/h downstream speed.
360? 40=9 hours return time
6. In still water, the speed of ship A and ship B is 26 km/h and 22 km/h respectively. The two ships set sail from Ping 'an Port, and B set sail two hours earlier than A. If the current speed is 6 kilometers per hour, how many hours after A sets sail, can it catch up with B?
(22+6)? 2=56 km catch-up distance
56? (26-22)= 14 hour catch-up time