SOLUTION: I have a new home 86 miles away. The movers left 12 minutes ago are traveling 50miles per hour I am leaving my house now and plan to drive 65 miles per hour. I want to reach the ho

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I have a new home 86 miles away. The movers left 12 minutes ago are traveling 50miles per hour I am leaving my house now and plan to drive 65 miles per hour. I want to reach the ho      Log On


   

Question 342187: I have a new home 86 miles away. The movers left 12 minutes ago are traveling 50miles per hour I am leaving my house now and plan to drive 65 miles per hour. I want to reach the house before the movers, which means that I will pass them on the road. Create a system of equations to show the distance of the movers at any given time
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Assume I have a stopwatch which I will start
when I leave house 12 min after movers.
My equation of motion is d%5B1%5D+=+65t
The equation for the movers is d%5B2%5D+=+50%2A%28t+%2B+12%2F60%29
Note that at t=0 when the stopwatch starts
d=0 for me, and d=10 for movers
To find the time on stopwatch when I pass the movers,
set my d%5B1%5D equal to their d%5B2%5D
65t+=+50%2A%28t+%2B+1%2F5%29
65t+=+50t+%2B+10
15t+=+10
t+=+2%2F3 hr
t+=+%282%2F3%29%2A60 min
t+=+40 min (time on stopwatch when I pass movers)
Here's a plot of the 2 equations:
+graph%28+500%2C+500%2C+-1%2C+2%2C+-10%2C+100%2C+65x%2C+50x+%2B+10%29+
When d%5B1%5D+=+86,
t+=+86%2F65
t+=+1.323 hr
and d%5B2%5D+=+50%2A%281.323+%2B+.2%29
d%5B2%5D+=+76.15 mi
86+-+76.15+=+9.85 mi
This is how far behind the mover is when I reach house