SOLUTION: billy and miranda are training at the track. billy can complete a lap in 40 seconds. miranda and billy begin at the same start/finish line and at the same time, but run in opposite

Question 403524: billy and miranda are training at the track. billy can complete a lap in 40 seconds. miranda and billy begin at the same start/finish line and at the same time, but run in opposite directions. Although different, their individual speeds remain constant and they pass each other every 15 seconds. miranda stops after finishing 12 laps. billy continues to run at the same rate.
-my task is to determine how many times miranda and billy passed each other exactly at the start/finish line during the time they were both running and how many more minutes and seconds and exactly how many morelaps billy will need to run to have run exactly the same distance that miranda ran.
*i tried to draw a diagram and i had miranda run the 12 laps and during those 12 laps i marked evert 15 seconds where they met, however i got diferent answers everytime i tried.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
billy can complete a lap in 40 seconds.
miranda and billy begin at the same start/finish line and at the same time,
but run in opposite directions.
Although different, their individual speeds remain constant and they pass each other every 15 seconds.
miranda stops after finishing 12 laps.
billy continues to run at the same rate.
-my task is to determine how many times miranda and billy passed each other
exactly at the start/finish line during the time they were both running and
how many more minutes and seconds and exactly how many more laps billy will
need to run to have run exactly the same distance that miranda ran.
:
Find out how long it takes M to complete one lap
After 15 sec, B completes or of one lap
therefore M has completed of one lap when the they meet in 15 sec
B to M speed ratio= 3:5
Time is inversely proportional to speed, let m = M's lap time
=
Cross multiply
5m = 5*40
m = 120/5
m = 24 sec for M to complete one lap
:
M completes 12 laps: 24 * 12 = 288 sec
B completes 12 laps: 40 * 12 = 480 sec
B runs; 480 - 288 = 192 sec longer than M to complete 12 laps
:
How many times will they meet during the 288 sec that M ran?
They met every 15 sec: 288/15 ~ 19 times
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