SOLUTION: At noon a horse and buggy headed north at 10 miles per hour. Two hours later, the roadster headed south from the same location at 30 miles per hour. At what time will the horse and

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Question 1128428: At noon a horse and buggy headed north at 10 miles per hour. Two hours later, the roadster headed south from the same location at 30 miles per hour. At what time will the horse and buggy be 80 miles from the roadster?
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs for for the roadster to
be 80 mi from horse & buggy
Let +d+ = distance in miles the roadster
travels in +t+ hrs
+10%2A2+=+20+ mi is the horse & buggy's head start
---------------------------
Equation for Horse & buggy:
(1) +80+-+d+-+20+=+10t+
Equation for roadster:
(2) +d+=+30t+
---------------------------
(1) +80+-+30t+-+20+=+10t+
(1) +40t+=+60+
(1) +t+=+1.5+
The roadster left at 2 pm
2 pm + 1.5 hrs = 3:30 pm
At 3:30 pm they are 80 mi apart
-----------------------------------
check:
(1) +80+-+d+-+20+=+10%2A1.5+
(1) +60+-+d+=+15+
(1) +d+=+45+ mi
and
(2) +d+=+30%2A1.5+
(2) +d+=+45+ mi
OK


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

80=10t%2B30%28t-2%29
80=10t%2B30t-60
40t=80%2B60
40t=140
t=140%2F40
t=3.5
answer:t=3.5h
PROOF:
80=10%2A3.5%2B30%283.5-2%29
80=35%2B30%2A1.5
80=35%2B45
80=80