This topic examines how to use a linear function to solve practical problems and how to use the undetermined coefficient method to find the analytical formula of the function. Note that the combination of numbers and shapes can deepen the understanding of the topic;
(1) When the ship speed =22+2=24 km/, the distance between the two ports can be obtained by multiplying the time, and the time for the speedboat to travel from Port B to Port A is 2 hours, from which the speed of the speedboat can be obtained, that is, the speed in reverse water, and then the speed of the speedboat in still water can be obtained;
(2) When the ship returns, the speed is the difference between the speed in still water and the water speed, and the distance is the distance between two ports, so that the arrival time can be calculated as time, and then the coordinates of C can be calculated, and then the analytical formula of the function can be obtained by the undetermined coefficient method;
(3) Then find the analytical expression of the function EF. According to the return distance 12km, that is, the difference between the function values of two functions is 12, the equation can be listed and the value of x can be found.
explain
Solution:
( 1)
The speed of the ship in still water = 3× (22+2) = 72km.
The speed of speedboat in still water = 72 ÷ 2+2 = 38 km/h.
(2)
The abscissa of point C =4+72÷(22-2)=7.6.
∴C(7.6,0),B(4,72)，
Let the analytical formula of BC line be y=kx+b(k≠0), then
7.6k+b=0
4k+b=72
Solution:
k=-20
b= 152
∴y=-20x+ 152(4≤x≤7.6)；
(3)
The speedboat departs for 3 hours or 3.4 hours, and the distance between the two ships is12km.