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).
:
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(36^2 + 27^2)}}} = 45; confirms our solution