SOLUTION: Carl and Kyle leave Kyle's house at the same time. Carl drives north and Kyle drives West. Carl's average speed is 9 mph slower than Kyle's. At the end of one hour, they are 45 mil

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Carl and Kyle leave Kyle's house at the same time. Carl drives north and Kyle drives West. Carl's average speed is 9 mph slower than Kyle's. At the end of one hour, they are 45 mil      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 275955: Carl and Kyle leave Kyle's house at the same time. Carl drives north and Kyle drives West. Carl's average speed is 9 mph slower than Kyle's. At the end of one hour, they are 45 miles apart. Find the average speed of Kyle. (Round off your answer to the nearest tenth).
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Carl and Kyle leave Kyle's house at the same time.
Carl drives north and Kyle drives West.
Carl's average speed is 9 mph slower than Kyle's.
At the end of one hour, they are 45 miles apart.
Find the average speed of Kyle. (Round off your answer to the nearest tenth).
:
Let s = K's driving speed
then
(s-9) = C's driving speed
:
Solve this as a right triangle: a^2 + b^2 = c^2
where the distance after 1 hr is:
a = 1s
b = 1(s-9)
c = 45
:
s^2 + (s-9)^2 = 45^2
A quadratic equation
s^2 + s^2 - 18s + 81 = 2025
:
2s^2 - 18s + 81 - 2025 = 0
:
2s^2 - 18s - 1944 = 0
Simplify, divide by 2
s^2 - 9s - 972 = 0
Fortunately this will factor
(s - 36)(s + 27) = 0
Positive solution
s = 36 mph is K's speed
:
:
Check solution using a calc:
Enter: sqrt%2836%5E2+%2B+27%5E2%29 = 45; confirms our solution