Question 976188
Albert and Bob ran a race of 440 yards.
 In the first trial Albert gave bob a start of 65 yards and won by 20 seconds.
 In the second trial Albert gave bob a start 34 seconds and bob won by 8 yards.
 Find the speeds of Albert and bob in yards per second
:
let a = Al's running speed (yds/sec)
let b = Bob's speed
:
Write a time equation for each scenario; time = dist/speed
:
A runs 440 yds while b runs 440 - 65 = 375 yds, beats him by 20 sec 
b's time - a's time = 20 sec
{{{375/b}}} - {{{440/a}}} = 20
:
b's travels 440 - 8 = 432 yds, while a travels 440 yds in 34 sec less time
{{{432/b}}} - {{{440/a}}} = 34

subtract the 1st equation from the 2nd equation
{{{432/b}}} - {{{440/a}}} = 34
{{{375/b}}} - {{{440/a}}} = 20
--------------------------------subtraction eliminates a, find b
{{{57/b}}} = 14
b = {{{57/14}}}
b = 4.07 yds/sec is Bob's speed
:
Find a using the 1st equation
{{{375/4.07}}} - {{{440/a}}} = 20
92.1376 - {{{440/a}}} = 20
-{{{440/a}}} = 20 - 92.1376
-{{{440/a}}} = -72.1376
{{{440/a}}} = 72.1376
a = {{{440/72.1376}}}
a = 6.1 yds/sec is Al's speed
:
:
Check this in the 2nd equation
{{{432/4.07}}} - {{{440/6.1}}} = 34
106.14 - 72.13 = 34.0 sec