SOLUTION: shelly and jack left from the same place at the same time and drove in opposite directions along a straight road. Jack traveled 15 miles per hour faster than shelly. After 3 hours,

Algebra ->  Real-numbers -> SOLUTION: shelly and jack left from the same place at the same time and drove in opposite directions along a straight road. Jack traveled 15 miles per hour faster than shelly. After 3 hours,      Log On


   

Question 175275: shelly and jack left from the same place at the same time and drove in opposite directions along a straight road. Jack traveled 15 miles per hour faster than shelly. After 3 hours, they were 315 miles apart. Find the rate at which each traveled.
Answer by agosset(4) About Me  (Show Source):
You can put this solution on YOUR website!
We know that Speed equals distance over time
Speed=Distance%2FTime
In this problem we are dealing with two speeds, Shelly's and Jack's
And we know that Jack's speed is 15 miles faster:
Jack's (J) = Shelly's (S) + 15
J=S%2B15
Then we know they have covered 315 miles (distance) after 3 hours (time)using their combined speeds.
Since they are traveling opposite directions we need to add their speeds:

J%2BS=Distance%2Ftime
We replace the known values for distance and speed:
J%2BS=315%2F3

Remember that J=S+15 so we replace J with the expression s+15
%28S%2B15%29+%2B+S+=+105
2s+%2B+15=105
2s=105-15
2s=90
s=90%2F2
s=45
And we know that Jacks is 15 more
J=S%2B15
J=45%2B15
j=60
Jack's speed= 60 Miles per hour
Rate= Speed
Jacks= 60 Miles per hour
Shelly's = 45 Miles per hour