Final answer:
The speed of the boat in still water and the speed of the current can be found by solving simultaneous equations created from the distances and times given for downstream and upstream travel. This requires algebra and an understanding of how to combine vectors of speed in opposite directions.
Step-by-step explanation:
To answer the question regarding the speed of the boat in still water and the speed of the current, we must apply our knowledge of river current problems, which typically involve algebra. The boat's speed in still water and the speed of the current can be treated as two different vectors. Since time, distance, and speed are related by the formula distance = speed × time, we can set up equations to solve for these unknowns.
Let's denote the speed of the boat in still water as b and the speed of the current as c. Downstream, the boat and current speeds add up, while upstream, the current speed subtracts from the boat speed. Using the given times and the fact that the distance is the same in both directions, we can set up the following equations:
(1) 21 = (b + c) × 3
(2) 21 = (b - c) × 7.
We can then solve the equations simultaneously to find the values of b and c. The boat's speed in still water and the current's speed are crucial pieces of information for solving this kind of problem. This example illustrates the common type of calculations involved in river current word problems.