SOLUTION: In a first race, A gives b a Headstart of 100 feet and overtakes him in four minutes. In the second race he gains 750 feet on B when B runs 9000 feet. Find the rate at which each r
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-> SOLUTION: In a first race, A gives b a Headstart of 100 feet and overtakes him in four minutes. In the second race he gains 750 feet on B when B runs 9000 feet. Find the rate at which each r
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Question 893076: In a first race, A gives b a Headstart of 100 feet and overtakes him in four minutes. In the second race he gains 750 feet on B when B runs 9000 feet. Find the rate at which each runs. Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Call the runners A and B
Let their speeds be and in feet / minute
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Start a stopwatch when A leaves
In the 1st race:
Let = the distance A runs when he overtakes B
A's equation:
(1)
B's equation:
(2)
================
In the 2nd race:
I think they both leave at the same time, so
Let = time in minutes until A is ft
ahead of B
------------------
A's equation:
(3)
B's equation:
(4)
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This is actually 4 equations with 4 unknowns,
so it is solvable
Substitute (1) into (2)
(2)
(2)
(2)
(2)
-----------------------
Substitute (4) into (3)
(4)
(3)
(3)
(3)
Divide both sides by
(3)
Substitute (2) int (3)
(3)
(3)
(3)
and, since
(2)
(2)
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A's speed is 325 ft/min
B's speed is 300 ft/min
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check:
(1)
(1)
(1) ft
and
(2)
(2)
(2)
(2) ft
OK
You can check (3) and (4)
