SOLUTION: A and B are running on a track having 8 laps to a mile. If they run in opposite directions, they meet every 20s. If they run in the same direction, it requires 3mins for A to overt
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Question 425938: A and B are running on a track having 8 laps to a mile. If they run in opposite directions, they meet every 20s. If they run in the same direction, it requires 3mins for A to overtake B. Find the rate of each in feet per second.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A and B are running on a track having 8 laps to a mile.
If they run in opposite directions, they meet every 20s.
If they run in the same direction, it requires 3mins for A to overtake B.
Find the rate of each in feet per second.
:
Let a = running speed of A, ft/sec
let b = running speed of B
:
Change 3 min to 180 sec
:
Size of circular track = * 5280 = 660 ft
:
Write a dist equation for each direction; dist = time * speed
:
20a + 20b = 660, opposite direction
180a - 180b = 660, same direction
:
multiply 1st equation by 9, add to 2nd equation
180a + 180b = 5940
180a - 180b = 660
-----------------------adding eliminates b, find a
360a = 6600
a = ft/sec is A's running speed
a = 18.333 or 18 ft/sec
then
20*18.333 + 20b = 660
366.66 + 20b = 660
20b = 660 - 366.66
20b = 293.333
b =
b = 14.67 ft/sec is B's running speed
:
:
We can check this by finding the total distance they ran in 20 sec
20*18.333 = 366.66 ft
20*14.667 = 293.34 ft
-----------------------
total dist: 660 ft
:
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