SOLUTION: Would you be able to help me with the following question? if i drive to the railway station at 80 km-1 i will be 15 min late for my train. If I drive at 110 km h-1 i will be 10

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Question 1026221: Would you be able to help me with the following question?
if i drive to the railway station at 80 km-1 i will be 15 min late for my train. If I drive at 110 km h-1 i will be 10 minutes early. How far do I live from the station?
Thanks,
Bob
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in hours that
will make you arrive on time
Let +d+ = your distance in miles
from the station
------------------
Equation for arriving late:
(1) +d+=+80%2A%28+t+%2B+1%2F4+%29+
Equation for arriving early:
(2) +d+=+110%2A%28+t+-+1%2F6+%29+
-----------------------
( note that I converted minutes to
fractions of an hour )
Substitute (1) into (2)
(2) +110%2A%28+t+-+1%2F6+%29+=+80%2A%28+t+%2B+1%2F4+%29+
Divide both sides by +10+
(2) +11%2A%28+t+-+1%2F6+%29+=+8%2A%28+t+%2B+1%2F4+%29+
(2) +11t+-+11%2F6+=+8t+%2B+2+
(2) +3t+=+12%2F6+%2B+11%2F6+
(2) +3t+=+23%2F6+
(2) +t+=+23%2F18+
------------------
Plug this result back into either equation
to get +d+
(1) +d+=+80%2A%28+t+%2B+1%2F4+%29+
(1) +d+=+80%2A%28+23%2F18+%2B+1%2F4+%29+
(1) +d+=+80%2A%28+46%2F36+%2B+9%2F36+%29+
(1) +d+=+80%2A%28+55%2F36+%29+
(1) +d+=+122.222+ mi
You live 122.222 mi from station
------------------
check answer:
(2) +d+=+110%2A%28+t+-+1%2F6+%29+
(2) +d+=+110%2A%28+23%2F18+-+3%2F18+%29+
(2) +d+=+110%2A%28+10%2F9+%29+
(2) +d+=+122.222+
OK
Hope I got it -you might want a 2nd opinion