SOLUTION: Pedro and Juan run at constant speeds along a circular track 1350 m in circumference. if they run in opposite directions, they meet every 3 minutes, while running in the same direc

Question 765136: Pedro and Juan run at constant speeds along a circular track 1350 m in circumference. if they run in opposite directions, they meet every 3 minutes, while running in the same direction they are together every 27 minutes. Determine the speed of Pedro.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Pedro and Juan run at constant speeds along a circular track 1350 m in
circumference. if they run in opposite directions, they meet every
3 minutes, while running in the same direction they are together
every 27 minutes.
Determine the speed of Pedro.
:
let p = P's speed
Let j = J's speed
:
When going in opposite directions they run a total of 1350 m in 3 min
When going in the same direction, the difference in the distance
they run in 27 min is 1350 m
:
Two dist equation (in meters)
3p + 3j = 1350
27p - 27j = 1350
:
Use elimination here, multiply the 1st equation by 9 and add
27p + 27j = 12150
27p - 27j = 1350
-----------------addition eliminates j, find p
54p = 13500
p = 13500/54
p = 250 m/min is P's speed
:
:
To check this find J's speed
3(250) + 3j = 1350
3j = 1350 - 750
j = 600/3
j = 200 m/min is J's speed
:
Find the distance each runs in 27 min
27(250) = 62500 m
27(200) = 54000 m
------------------
difference: 1350 m
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