Question 883280
Albert and Bob ran a race of 440 yards.
:
Let a = A's speed
Let b = B's speed
:
In the first trial, Albert gave Bob a headstart of 65 yards and won by 20 seconds.
Write at time equation; time = dist/speed
B only ran 440 - 65 = 375 yds
:
b's time - a's time = 20 sec
{{{375/b}}} - {{{440/a}}} = 20
:
In the second trial, Albert gave Bob a headstart of 34 seconds and Bob won by 8 yards.
B ran 440 - 8 = 432 yrds
{{{432/b}}} - {{{440/a}}} = 34
:
We can use elimination here
{{{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 B's running speed
:
Find a
{{{432/4.07}}} - {{{440/a}}} = 34
106.14 - {{{440/a}}} = 34
{{{440/a}}} = 34 - 106.14
{{{440/a}}} = 72.14
a = {{{440/72.14}}}
a = 6.1 yds/sec is A's running speed
:
:
See if this works
{{{375/4.07}}} - {{{440/6.1}}} = 20
92 - 72 = 20