00:01
To solve this question, first of all we will let here the woman length at a distance, a distance 6 minus x meter from the restaurant and we have to create a diagram over here.
00:24
So let's take this as a distance where the woman length is here at this point.
00:32
So we'll take this distance as x and here the remaining is 6.
00:40
So the height is given as 3.
00:44
So at a distance of 6 minus x meter from the rest of it.
00:58
And from this we will solve our first part of the question where we need to find the total required time.
01:05
Total time required by a woman to reach the resquend and that will be calculated from as t is equal to within the square root as the total distance is 9 plus x squared divided by 2 added by 6 plus x i'm sorry 6 minus x this is minus x divided by 3.
01:49
So now for time to be minimum, be minimum, we will find our derivative d t by d x and that is equal to 0.
02:06
So thereafter our ability for d t by d x is equal to 1 multiplied by x divided by 2 within the square root 9 plus x square minus 1 upon 3 will be equal to 0.
02:28
And when we compute this as x divided by 2 square root 9 plus x square will be equal to 1 upon 3 and getting cross multiplied as 3 x is equal to 2 square root 9 plus x squared.
02:47
So we will square both sides.
02:51
So 3x square is equal to square of 2 within the square root 9 plus x squared to the polar square.
03:00
So now this will be as 9x square is equal to 4 in the bracket 9 plus x squared square square root is removed and then we will open our equation as 9x square is equal to 36 plus 4x square.
03:15
So we are having here 5x square is equal to 36.
03:21
So then our value for x will be equal to 36 is a square of 6 within the square root of 5.
03:31
So then this is the value as the distance.
03:36
So our answer for part a is x is equal to 6 upon square root 5m meter from the point he shares the distance.
03:48
So this is the first solution of the question.
03:50
Now let's find out our second answer for part b.
03:55
Here we will take the woman as let the woman rose at v meter per hour and v miles per hour and land somewhere.
04:22
So here somewhere at x.
04:26
Again we will find our time that is square root 9 plus x squared divided by v plus 6 minus 3 divided by 3.
04:37
And this will be our equation 1.
04:39
So when we simplify this equation we will get here, square root of 9 plus x squared divided by v is equal to t minus 6 minus x divided by 3...