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.
:
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/a}}} - {{{30/b}}} = 1
:
Write a time equation when A has doubled his pace
B's time -  A's time = 2 hrs
{{{30/b}}} - {{{30/(2a)}}} = 2
Reduce the fraction
{{{30/b}}} - {{{15/a}}} = 2
:
Arrange these two equations to use elimination here
{{{30/a}}} - {{{30/b}}} = 1
{{{-15/(a)}}} + {{{30/b}}} = 2
-----------------------Addition eliminates b, find a
{{{15/a}}} = 3
15 = 3a
a = 15/3
a = 5 km/hr, A's original speed
;
Find b using the 1st original equation
{{{30/5}}} - {{{30/b}}} = 1
6 - {{{30/b}}} = 1
 -{{{30/b}}} = 1 - 6
 -{{{30/b}}} = -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)
{{{30/6}}} - {{{30/10}}} = 
5 - 3 = 2 hrs
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Hopefully we have restored your nerves to an agreeable level. C