SOLUTION: Please help me with this problem as fast as you can. Your effort is appreciate. :) ~Carolyn drove from her home to school at 40 mph and was 10 minutes late. The next day she drove

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Question 770904: Please help me with this problem as fast as you can. Your effort is appreciate. :)
~Carolyn drove from her home to school at 40 mph and was 10 minutes late. The next day she drove to school at 60 mph and was 10 minutes early. How far is far Carolyn's school from her home?
P.S. when u help me can you please please send answer,explanation and how you get the answer. Thank you!
Sincerely, desperately hoping for an answer ASAP.
Found 2 solutions by josmiceli, mananth:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = the time in hours which
would make her arrive on time
----------------------------
+t+%2B++10%2F60++ = her time in hrs when
she drives +40+ mi/hr
----------------------
+t+-++10%2F60++ = her time in hrs when
she drives +60+ mi/hr
----------------------
Let +d+ =distance in miles from home to school
----------------------
Equation for driving +40+ mi/hr:
(1) +d+=+40%2A%28+t+%2B+10%2F60++%29+
Equation for driving +60+ mi/hr:
(2) +d+=+60%2A%28+t+-+10%2F60++%29+
--------------------------
(1) +d+=+40%2A%28+t+%2B+1%2F6++%29+
(1) +d+=+40t+%2B+20%2F3+
and
(2) +d+=+60%2A%28+t+-+1%2F6++%29+
(2) +d+=+60t+-+10+
-------------------
By substitution:
(2) +40t+%2B+20%2F3+=+60t+-+10+
(2) +20t+=+20%2F3+%2B+10+%7D%7D%0D%0A%282%29+%7B%7B%7B+20t+=+20%2F3+%2B+30%2F3+
(2) +20t+=+50%2F3+
(2) +t+=+5%2F6+
---------------
Plug this result back into either equation:
(2) +d+=+60%2A%28+5%2F6+-+1%2F6++%29+
(2) +d+=+60%2A%28+2%2F3+%29+
(2) +d+=+40+
The distance in miles from home to school is 40 mi
check:
(1) +d+=+40%2A%28+t+%2B+1%2F6++%29+
(1) +40+=+40%2A%28+t+%2B+1%2F6++%29+
(1) +40+=+40%2A%28+5%2F6+%2B+1%2F6++%29+
(1) +40+=+40%2A1+
OK


Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Carolyn drove from her home to school at 40 mph and was 10 minutes late. The next day she drove to school at 60 mph and was 10 minutes early. How far is far Carolyn's school from her home?

Let the required time to reach be t hours
Part I
speed = 40 mph
10 minutes = 10/60 hours = 1/6 hours
Actual time taken = with speed of 40 mph = t+1/6
Distance = speed * time
40%2A%28t%2B%281%2F6%29%29
Part II
speed = 60 mph
time = t-(1/6)
distance+=+60+%2A+%28t-%281%2F6%29%29

40%2A%28t%2B%281%2F6%29%29=+60+%2A%28t-%281%2F6%29%29
Distance is same. so equate distance

40%2A%286t%2B1%29%2F%286%29=60%2A%286t-1%29%2F%286%29
multiply by 6
40((6t+1))=60(6t-1))
240t+40=360t-60
360t-240t=60+40
120t=100
t= 100/120
t= 5/6 hours
Calculate distance
D=+40%2A%28t%2B%281%2F6%29%29
plug t
D= 40*(5/6 +1/6)
=40 miles
Distance from home = 40 miles