Question 559649: monica drove to work on monday at 40 miles per hour and arrived one minute late. she left the same time on tuesday, drove at 45 miles per hour, and arrived one minute early. how far does monica drive to work?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! monica drove to work on monday at 40 miles per hour and arrived one minute late. she left the same time on tuesday, drove at 45 miles per hour, and arrived one minute early. how far does monica drive to work?
Let time to be be taken to reach on time be t
Let distance be x miles
monica drove to work on monday at 40 miles per hour and arrived one minute late.
x/40 = t+1/60
multiply by 120
3x=120t+2
3x-120t=2.................1
monica drove to work on Tuesday at 45 miles per hour and arrived one minute early.
x/45 = t-1/60
multiply by 180
4x = 180t-3
4x-180t=-3..................2
solve for x &t
Multiply (1)by 4 and (2)3
12x-480t=8
12x-540t=-9
60 t=17
t= 17/60
plug t
x= 12 miles
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
monica drove to work on monday at 40 miles per hour and arrived one minute late.
she left the same time on tuesday, drove at 45 miles per hour, and arrived one minute early.
how far does monica drive to work?
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Let d be the distance Monica drives to work, in miles.
Driving at the speed of 40 mph, he spends  hours.
Driving at the speed of 45 mph, he spends  hours.
The difference of these time intervals is 2 minutes, or  of an hour.
So, we write this equation
- = .
Multiply both sides by 360. You will get
9d - 8d = 12,
d = 12.
ANSWER. The distance is 12 miles.
Solved.
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It is a standard classic elegant solution to this problem.
This problem is designed, created and exists to be solved
by the method shown in my post.
The problem is created to teach students solving similar problems
by using "time equation". Learning this method, students will be
fascinated by its beauty. That's the point of this task.
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