Ared kite is 100 feet off the ground and is rising 8 feet per second. a blue kite is 180 feet off the ground and is rising 5 feet per second. how long will it take for the red kite to be higher than the blue kite

From the information given you can form two linear equations. 
Red kite: Y = 8x + 100 
Blue Kite: Y = 5x + 180 

you are looking for where these two lines intersect on a graph. 

Each equation gives you a value of y so you can take one and put it in the place of the other 

Ex., 8x + 100 = 5x +180 

rearrange this and you get 3x - 80 = 0

then isolate x:
1) 3x = 80 
2) x = 80/3
3) x = 26.7

Now, put your X value into either of the original equations to find Y

Y = 8x + 100
Y = 8(26.7) + 100
Y = 313.6

to check your answer you can do a simple left side right side check 

313.6 = 5(26.7) + 180 

313.6 = 133.5 + 180

313.6 = 313.5 

** this counts as correct, the difference in decimal is due to rounding