SOLUTION: Two motorists A and B race around a circular mile track starting at the same positions and at the same time. When traveling in the opposite, they are together every 18 seconds, and

Question 545857: Two motorists A and B race around a circular mile track starting at the same positions and at the same time. When traveling in the opposite, they are together every 18 seconds, and when traveling in the same direction, they are together every 90 seconds. Find their speeds in mph.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two motorists A and B race around a circular mile track starting at the same positions and at the same time.
When traveling in the opposite, they are together every 18 seconds, and when traveling in the same direction, they are together every 90 seconds.
Find their speeds in mph.
:
Let a = speed of A
Let b = speed of B
:
They want the answer in mph, change seconds to hours
= .005 hrs
= .025 hrs
:
write a distance equation for each scenario
.005(a + b) = 1, (opposite directions)
.025(a - b) = 1, (same direction)
:
In each equation: divide both sides by .005, divide the 2nd equation by .025, results:
a + b = 200
a - b = 40
------------adding eliminates b, find a
2a = 240
a = 240/2
a = 120 mph for A
and
a + b = 200
120 + b = 200
b = 200 - 120
b = 80 mph for B

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