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Question 1207782: 1. Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. During Explaining Concepts:Discussion and Writing your run, your average speed is 6 miles per hour, and during your bicycle race, your average speed is 25 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the distance of the bicycle race?
2. In the 1984 Olympics, C.Lewis of the United States won the gold medal in the 100-meter race with a time of 9.99 seconds. In the 1896 Olympics,Thomas Burke,also of the United States, won the gold medal in the 100-meter race in 12.0 seconds. If they ran in the same race repeating their respective times, by how many meters would Lewis beat Burke?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
1. Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race.
During your run, your average speed is 6 miles per hour, and during your bicycle race,
your average speed is 25 miles per hour. You finish the race in 5 hours.
What is the distance of the run? What is the distance of the bicycle race?
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Let "t" be the time running, in hours.
Then the time cycling is (5-t) hours.
The total distance equation is
6t + 25(5-t) = 87 miles.
Simplify and find "t"
6t + 125 - 25t = 87,
125 - 87 = 25t - 6t
38 = 19t
t = 38/19 = 2 hours.
So, you run 2 hours and cycle 5-2 = 3 hours.
The distance running is 6*2 = 12 miles. The distance cycling is 25*3 = 75 miles. ANSWER
Solved.
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2. In the 1984 Olympics, C.Lewis of the United States won the gold medal in the 100-meter race
with a time of 9.99 seconds. In the 1896 Olympics,Thomas Burke,also of the United States,
won the gold medal in the 100-meter race in 12.0 seconds.
If they ran in the same race repeating their respective times, by how many meters would Lewis beat Burke?
~~~~~~~~~~~~~~~~~~~~~
C.Lewis finished 12 - 9.99 = 2.01 seconds ahead of Thomas Burke.
Hence, C.Lewis beat Burke by  = 16.75 meters. ANSWER
Here the ratio  is the Burke' average speed in meters per second.
Solved.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
1. Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. During Explaining Concepts:Discussion and Writing your run, your average speed is 6 miles per hour, and during your bicycle race, your average speed is 25 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the distance of the bicycle race?
2. In the 1984 Olympics, C.Lewis of the United States won the gold medal in the 100-meter race with a time of 9.99 seconds. In the 1896 Olympics,Thomas Burke,also of the United States, won the gold medal in the 100-meter race in 12.0 seconds. If they ran in the same race repeating their respective times, by how many meters would Lewis beat Burke?
I'll do no. 1, ONLY!
Let distance of run, be D
Then, distance of bicycle race = 87 - D (Total distance of the biathlon is 87 miles)
As  , it follows that the: 
This gives us the following TIME equation:
 ----- Substituting D for RUN-DISTANCE, 6 for RUN-SPEED, "87 - D" for
RACE-DISTANCE, 25 for RACE-SPEED, and 5 for BIATHLON-TIME
25D + 6(87 - D) = 5(150) ----- Multiplying by LCD, 150
25D + 522 - 6D = 750
25D - 6D = 750 - 522
19D = 228
RUN-DISTANCE, or 
RACE-DISTANCE = 87 - D = 87 - 12 = 75 miles
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