00:01
In this problem, we are provided that there exists a cottage which can be denoted by sea along a straight shoreline such that there is a point q on this shoreline at a distance of 3 km east from the cottage and 2 kilometers north of this point q there exists an island which we denote by r.
00:30
Emma wants to reach the island r from the cottage c by means of walking as well as swimming.
00:43
Emma walks at a rate of 4 km per hour and she swims at a rate of 3 km per hour.
00:55
She decides to walk up to a point p which can be assumed to be at a distance of x from the cottage.
01:03
And from the point p up to the island r, she swims the rest of the way.
01:11
The question here is to find the minimum possible time which can be denoted by t of x for emma to travel from the cottage c to the island r.
01:25
Let us begin by calculating the time t1 which is the time she takes for walking.
01:31
We can find this by using the formula the time t equals to the distance divided by the speed.
01:46
Here, t1 will thus equal to the distance x divided by the speed 4.
01:53
Likewise, we can calculate the time t2, which is the time m .r takes for swimming.
02:01
In order to calculate this, we need to know the distance pr, which can be found using.
02:06
Using pythagr theorem.
02:09
Since the distance qr equals to 2 km and the distance pq equals to 3 minus x kilometer, we have pr to be positive square root of 3 subtracted with x the whole squared plus 2 squared which is 4...