SOLUTION: From the park, Janet and Terry started jogging at constant rates. Janet goes a 5 km/hr in the direction of N 48 degrees E while Terry goes in the direction of S 72 degrees E. After

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Question 593927: From the park, Janet and Terry started jogging at constant rates. Janet goes a 5 km/hr in the direction of N 48 degrees E while Terry goes in the direction of S 72 degrees E. After one hour, they are 7 km. apart. How fast did Terry jog?
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
It is not clear to me what "N 48 degrees E" and "S 72 degrees E" mean. If my guess is right then the angle between Janet's path and Terry's path is 60 degrees. If this is not correct, then replace the 60's you see below with whatever the correct number of degrees is. If you do not know how to find this angle, then you'll have to ask for help from someone else or re-post your question and explain what "N 48 degrees E" and "S 72 degrees E" mean.

It might help to draw a diagram. Draw a triangle and name the vertices as A, B and C. Let A be where they started. Let B be where Janet was after an hour. And let C be where Terry was after that same hour.

Since Janet was running at 5km/hr for one hour, then the length of AB must be 5km. And since they were 7km apart after the hour the length of BC is 7km. Mark the sides of the triangle with these lengths and mark angle A with 60 degrees.

We are looking to find the length of AC. This will give us the distance traveled by Terry. And since she ran for an hour, it will also be her speed.

So we have two sides and an angle of a triangle and we are looking for the third side. This is a job for the Law of Cosines:
where
A is an angle and "a" is the side opposite that angle,
B is an angle and "b" is the side opposite that angle,
C is an angle and "c" is the side opposite that angle
Since AC is opposite angle B, it would be called "b" in this formula. Similarly AB would be called "c".
(Note: Since angle A is the only angle we know, we have to use this form of the law.)

Inserting our numbers into this formula we get:

which simplifies as follows:

Now we solve for b. This is a quadratic equation so we want one side to be zero. Subtracting 49 from each side we get:

Now we factor (or use the Quadratic Formula). This factors fairly easily:
0 = (b - 8)(b + 3)
From the Zero Product Property we know that this product can be zero only if one of the factors is zero. So:
b - 8 = 0 or b + 3 = 0
Solving these we get:
b = 8 or b = -3
Since "b" is a distance we do not want negative values. So we reject b = -3. So Terry ran 8 km during the hour making her speed 8 km/hr.