Question 886743
 A and B are running on a track having 8 laps to the mile.
If they run in opposite directions they meet every 20 seconds.
If they run in the same direction it requires 3 minutes for A to overtake B.
Find the rate of each in per second.
:
Find the no. of ft per lap: {{{5280/8}}} = 660 ft
:
Let a = A's speed in ft/sec
Let b = B's speed
:
3 min = 180 sec
:
When running in opposite directions, their relative speed is the sum
When running in the same direction, their relative speed is the difference
:
Write a distance equation for each way; dist = time * relative speed
20(a + b) = 660
and
180(a - b) = 660
:
multiply the 1st equation by 9
180(a + b) = 5940
180(a - b) = 660
Distribute
180a + 180b = 5940
180a - 180b = 660
-------------------adding eliminates b, find a
360a = 6600
a = 6600/360
a = 18{{{1/3}}} ft/sec is A's running speed
:
Find b using the 1st original equation
20(18.333 + b ) = 660
simplify, divide both sides by 20
18.333 + b = 33
b = 33 - 18.333
b = 14{{{2/3}}} ft/sec is B's speed
:
:
Confirm that in the 2nd equation
180(18.333 - 14.667) = 660
180(3.667) = 660
659.998 ~ 660