SOLUTION: I need to see the step by step solution to solving this and i need this to be solved by graphing so if a graph could be made and shown to me I'd love it! Eric can ride 162 miles

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I need to see the step by step solution to solving this and i need this to be solved by graphing so if a graph could be made and shown to me I'd love it! Eric can ride 162 miles      Log On


   



Question 838436: I need to see the step by step solution to solving this and i need this to be solved by graphing so if a graph could be made and shown to me I'd love it!
Eric can ride 162 miles on flat ground in 6 hours with a good breeze at his back. It takes him 10 hours to go 90 miles with the same breeze working against him. How fast is Eric going on a bike and how fast is the wind speed?
please tell me how to setup the graph and solve from the graph
THANKS

Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Have you ever ridden a bike?
What's the relation between windspeed and groundspeed?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = Eric's speed on a bike with no wind in mi/hr
Let +w+ = the speed of the wind in mi/hr
------------------------------------
Equation riding with the wind:
(1) +162+=+%28+s+%2B+w+%29%2A6+
Equation riding against the wind:
(2) +90+=+%28+s+-+w+%29%2A10+
-----------------------
(1) +6s+%2B+6w+=+162+
(1) +3s+%2B+3w+=+81+
(1) +s+%2B+w+=+27+
and
(2) +10s+-+10w+=+90+
(2) +s+-+w+=+9+
--------------------
Add the equations:
(2) +s+-+w+=+9+
(1) +s+%2B+w+=+27+
+2s+=+36+
+s+=+18+
and
(2) +s+-+w+=+9+
(2) +18+-+w+=+9+
(2) +w+=+9+
-------------------
Riding with the wind, Eric is going +18+%2B+9+=+27+ mi/hr
Riding against the wind, Eric is going +18+-+9+=+9+ mi/hr
The wind speed is +9+ mi/hr
--------------------------------
Here's a plot of (1) and (2):
+w+ is on the horizontal axis
+s+ is on the vertical axis
+graph%28+400%2C+400%2C+-6%2C+30%2C+-10%2C+50%2C+x+%2B+9%2C+-x+%2B+27+%29+
check answers:
(1) +162+=+%28+s+%2B+w+%29%2A6+
(1) +162+=+%28+18+%2B+9+%29%2A6+
(1) +162+=+27%2A6+
(1) +162+=+162+
-------------------------
(2) +90+=+%28+s+-+w+%29%2A10+
(2) +90+=+%28+18+-+9+%29%2A10+
(2) +90+=+9%2A10+
(2) +90+=+90+
OK