SOLUTION: A takes 1 hour longer than B to walk 30km, A's pace was doubled,then A would take 2 hours less than B. find their rates of walking. pls. help me to solve this problem it's gettin

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A takes 1 hour longer than B to walk 30km, A's pace was doubled,then A would take 2 hours less than B. find their rates of walking. pls. help me to solve this problem it's gettin      Log On


   

Question 588205: A takes 1 hour longer than B to walk 30km, A's pace was doubled,then A would take 2 hours less than B. find their rates of walking. pls. help me to solve this problem it's getting on my nerves....
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A takes 1 hour longer than B to walk 30km,
A's pace was doubled, then A would take 2 hours less than B.
find their rates of walking.
:
let a = A's walking pace (km/hr)
let b = B's walking pace
:
Write a time equation for their normal pace; Time = dist/speed
A's time - B's time = 1 hr
30%2Fa - 30%2Fb = 1
:
Write a time equation when A has doubled his pace
B's time - A's time = 2 hrs
30%2Fb - 30%2F%282a%29 = 2
Reduce the fraction
30%2Fb - 15%2Fa = 2
:
Arrange these two equations to use elimination here
30%2Fa - 30%2Fb = 1
-15%2F%28a%29 + 30%2Fb = 2
-----------------------Addition eliminates b, find a
15%2Fa = 3
15 = 3a
a = 15/3
a = 5 km/hr, A's original speed
;
Find b using the 1st original equation
30%2F5 - 30%2Fb = 1
6 - 30%2Fb = 1
-30%2Fb = 1 - 6
-30%2Fb = -5
30 = 5b
b = 30/5
b = 6 km/hr is B's original speed
:
:
Check this when A doubles his speed (10 km/hr)
30%2F6 - 30%2F10 =
5 - 3 = 2 hrs
:
Hopefully we have restored your nerves to an agreeable level. C