SOLUTION: A bus left the city at 8:00am,traveling at 70km/h.Another bus,traveling in the opposite direction at 55km/h,left at 11:00am.At what time were the buses 460km apart?

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Question 1107731: A bus left the city at 8:00am,traveling at 70km/h.Another bus,traveling in the opposite direction at 55km/h,left at 11:00am.At what time were the buses 460km apart?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Start a stopwatch when the 2nd
bus leaves the city at 11 AM.
Let +t+ = the time in hrs on the
stopwatch when the buses are
460 km apart
Let +d%5B1%5D+ = distance in km the 1st bus travels
from 8 AM to 11 AM
Let +d+ = distance in km the 2nd bus travels
during time +t+ on the stopwatch
-----------------------------------------
Equation for the 1st bus from 8 AM to 11 AM
(1) +d%5B1%5D+=+70%2A3+
Equation for the 2nd bus:
(2) +d+=+55t+
Equation for the 1st bus during time +t+ on stopwatch
(3) +460+-+d%5B1%5D+-+d+=+70t+
------------------------------------------------------
(1) +d%5B1%5D+=+210+
Plug (2) into (3)
(3) +460+-+210+-+55t+=+70t+
(3) +250+-+55t+=+70t+
(3) +125t+=+250+
(3) +t+=+2+
------------------------------------------------------
2 hrs after 11 AM, or at 1 PM, the buses are 460 km apart
------------------------------------------------------
check the answer:
(2) +d+=+55t+
(2) +d+=+55%2A2+
(2) +d+=+110+ km
The first bus travels +460+-+110+=+560+ km from
8 AM to 1 PM, or 5 hrs
+350+=+r%2A5+
+r+=+70+ km/hr
OK