SOLUTION: 1a.Stella is having a race with Tess. Stella gives Tess a 5o foot head start. Stella runs at 14.3 feet per second and Tess runs at 12.5 feet per second. .Write a system of equati

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: 1a.Stella is having a race with Tess. Stella gives Tess a 5o foot head start. Stella runs at 14.3 feet per second and Tess runs at 12.5 feet per second. .Write a system of equati      Log On


   

Question 512112: 1a.Stella is having a race with Tess. Stella gives Tess a 5o foot head start. Stella runs at 14.3 feet per second and Tess runs at 12.5 feet per second. .Write a system of equations for the two sisters distances.
b.How far will they be from the start when Stella catches Tess?
c. How lon should the race be in order for it to be a close call.


I think part a is stella 14.3x - 50=y
and I am guessing
Tess is 12.5x=y
Please help!!
Answer by josmiceli(9817) About Me  (Show Source):
You can put this solution on YOUR website!
You have the right idea
To picture the situation, pretend you start a stopwatch
when Stella leaves.
Both will run different distances but for the same amount of time
Call this time +t+
Call the distance Stella runs +d+
-------------------
given:
Stella's equation:
(1) +d+=+14.3t+
Tess's equation:
(2) +d+-+50+=+12.5t+
-----------------
(b)
Substitute (1) into (2)
(2) +14.3t+-+50+=+12.5t+
(2) +1.8t+=+50+
(2) +t+=+27.778+ sec
and
(1) +d+=+14.3%2A27.778+
(1) +d+=+397.22+ ft
(c)
+27.778+ sec
--------------------
check answers:
(1) +d+=+14.3t+
(1) +397.22+=+14.3%2A27.778+
(1) +397.22+=+397.22+
and
(2) +d+-+50+=+12.5t+
(2) +397.22+-+50+=+12.5%2A27.778+
(2) +347.22+=+347.22+
OK