Give some students a basket of apples. If everyone has four apples, there are only nine left. If everyone has six apples, the last student will get less than three apples. Find out the number of students and apples.
A school-run factory has produced a batch of new products, and there are two sales schemes. Scheme 1: you can make a profit of 30,000 yuan by selling this batch of products at the beginning of this semester, and then reinvest the invested funds and the 30,000 yuan you have earned in this batch of products, and make a profit of 4.8% by the end of this semester; Option 2: If you sell this batch of products at the end of this semester, you can make a profit of 35,940 yuan, but you need to pay 0.2% of the invested capital as the storage fee. Q:
(1) When the investment of this batch of products is RMB, the profits of Scheme I and Scheme II are the same?
(2) According to the required investment, discuss which scheme I and scheme II will benefit more.
Two tourist passenger ships A and B set off from a port in Taiwan Province Province for Xiamen at the same time. A sail along a straight line 180 nautical miles to Xiamen; B bypassed Hong Kong on the original route and later sailed 720 nautical miles in Xiamen. As a result, B arrived in Xiamen 20 hours later than A. It is known that speed B is 6 nautical miles faster than speed A, so what is the speed of passenger ship A (the speed of both passenger ships is greater than 16 nautical miles per hour)?
In order to broaden students' horizons, a school organized students to walk 6 kilometers from school to visit the Science and Technology Exhibition Hall. I walked less when I came back than when I went 1 km. It took me half an hour to get back. Find the walking speed of students when they return.
The railway distance between cities A and B is 1, 600km. After technical transformation, the train has accelerated. After speeding up, the speed is increased by 20km/h, and the travel time from city A to city B is reduced by 4 hours. Under the existing safety conditions, the safe running speed of this railway should not exceed 1, 40km/h. Please use your mathematical knowledge to show that the train can run again under the existing conditions of this railway.
Do these questions have practical significance?
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