SOLUTION: A man can ride his bike 18 miles in the same time it takes him to run 6 miles. He can ride his bike 10 mph faster than he can run. How fast can he ride his bike?

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Question 929435: A man can ride his bike 18 miles in the same time it takes him to run 6 miles. He can ride his bike 10 mph faster than he can run. How fast can he ride his bike?
Found 2 solutions by TimothyLamb, MathTherapy:
Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
x = biking speed
y = running speed
---
s = d/t
t = d/s
---
bike:
t = 18/x
---
run:
t = 6/y
---
18/x = 6/y
18y = 6x
x = y + 10
---
put the system of linear equations into standard form
---
6x - 18y = 0
x - y = 10
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = biking speed = 15 mph
y = running speed = 5 mph
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A man can ride his bike 18 miles in the same time it takes him to run 6 miles. He can ride his bike 10 mph faster than he can run. How fast can he ride his bike?
Let biking speed be S

Then running speed is: S – 10

Therefore, 

18(S – 10) = 6S -------- Cross-multiplying

18S – 180 = 6S

18S – 6S = 180

12S = 180

S, or biking speed = , or  mph

You can do the check!! 

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