Hello, mathshelpneeded!
This is not an easy one . . .
Code:
M*

6t 

A*
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 \
5006t  \D
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 x \
N*      *B
8t
Cyclist starts at and goes south at 6 m/s.
In seconds, he has gone m to point .
Cyclist starts at and goes east at 8 m/s.
In seconds, he has gone m to point .
We want the problem in terms of , not .
In right triangle
We have: .
Factor: . [1]
We also have: . [2]
Substitute [1] into [2]: . (a)
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
We have: .
Then: .
We have: .
Then: .
Since , we have: .
. . Hence: .
Therefore: . (b)