SOLUTION: Suppose you have entered a 96 mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 9 mile per hour, and during your bicycle race, you

Question 830225: Suppose you have entered a 96 mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 9 mile per hour, and during your bicycle race, you average velocity is 29 miles per hour. You finish the race in 4 hours. What is the distance of the run? What is the distance of the bicycle race
what is the distance of the run in miles

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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x = run distance
y = bike distance
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s = d/t
t = d/s
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run:
t1 = x/9
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bike:
t2 = y/29
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total time:
t1 + t2 = 4
x/9 + y/29 = 4
---
total distance:
x + y = 96
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linear system:
(1/9)x + (1/29)y = 4
x + y = 96
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put the system of linear equations into standard form:
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0.111111x + 0.034483y = 4
x + y = 96
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copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = run distance = 9 miles
y = bike distance = 87 miles
---
Solve and graph linear equations:
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---
Solve quadratic equations, quadratic formula:
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---
Solve systems of linear equations up to 6-equations 6-variables:
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