SOLUTION: Soren had a 36 mile head start. If Eric caught him in 3 hrs, how fast was Eric traveling if his speed was 2x Sorens? I know D=RT. I assume they both went the same distance bec

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Question 602880: Soren had a 36 mile head start. If Eric caught him in 3 hrs, how fast was Eric traveling if his speed was 2x Sorens?
I know D=RT. I assume they both went the same distance because Eric caught up. I made the equation 2 different ways. The first one was like this:
RT=RT
(Sorens RT)=(Erics RT) I came up with 1/2, and I know this is not right.
I then tried (Sorens RT)=(Erics RT)+36, and I get a -12. I am not sure what I am doing wrong. Can you please help me?
Thanks,
Sheila
Found 2 solutions by josmiceli, scott8148:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Soren's head start was +36+ mi
Start a stop watch when Eric leaves.
Let +d+ = distance that Eric travels
Let +s+ = Soren's speed
They will both travel for the same amount of time, +3+ hrs
until Soren is caught.
Soren's equation:
(1) +d+-+36+=+s%2A3+
Eric's equation:
(2) +d+=+2s%2A3+
---------------
This is 2 equations and 2 unknowns, so it's solvable
Substitute (2) into (1)
(1) +6s+-+36+=+3s+
(1) +3s+=+36+
(1) +s+=+12+
+2s+=+24+
Eric's speed is 24 mi/hr
check:
(1) +d+-+36+=+s%2A3+
(1) +d+-+36+=+12%2A3+
(1) +d+=+36+%2B+36+
(1) +d+=+72+
and
(2) +d+=+2s%2A3+
(2) +d+=+2%2A12%2A3+
(2) +d+=+72+
OK

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"Soren had a 36 mile head start" ___ so they were not traveling the same distance

E * 3 = [(E/2) * 3] + 36

multiplying by 2 (to clear fraction) ___ 6E = 3E + 72