SOLUTION: I have this word problem here that is really confusing to me. I feel like I know how to do it but I just cant seem to figure it out. The number of minutes a freights train take

Question 99222This question is from textbook
: I have this word problem here that is really confusing to me. I feel like I know how to do it but I just cant seem to figure it out.
The number of minutes a freights train takes to pass an intersection varies directly with the number of cars in the train. A 150-car train passes in 3 min. How long will a 210-car train take to pass?
I can't seem to get an equation or anything to start out with. Would you please help me ? This question is from textbook

Found 2 solutions by checkley71, bucky:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
150/3=210/X NOW CROSS MULTIPLY
150X=3*210
150X=630
X=630/150
X=4.2 MINUTES FOR THE TRAIN TO PASS.

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let's look at it analytically.
.
Convert the 3 minutes to seconds. Since there are 60 seconds in a minute, 3 minutes is
equal to 60 + 60 + 60 = 180 seconds.
.
150 cars go past in that 180 seconds. How many seconds does it take for a single car to
go past? We are looking for an answer of seconds per car, so we put the 180 seconds over
the number of cars to get the units of seconds per car:
.
AMP Parsing Error of [(180 sec)/(150 car) = (180/150)*(sec)/(car)= (18/15)*(sec)/(car) = 6/5*(sec)/(car) = 1.2(sec)/(car)]: Invalid function ')/(car)=(18/15)*(sec)/(car)=6/5*(sec)/(car)=1.2(sec)/(car)': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70. .
.
So each car takes 1.2 seconds to pass.
.
If the train consists of 210 cars at 1.2 seconds for each car the time for the entire train
to pass will be 1.2 seconds per car times 210 cars:
.

.
and if you divide 252 seconds by 60 seconds per minute you get an answer of 4.2 minutes for
the 210 car train to pass.
.
Another way you can look at it is ... how many times bigger than a 150 car train is a 210 car
train? Set up the ratio:
.

.
The 210 car train is 1.4 times the size of the 150 car train. Therefore it should take
1.4 times as much time as the 150 car train to pass. Since the 150 car train passed in
3 minutes, the 210 car train should take 3 times 1.4 = 4.2 minutes to pass, and that agrees
with the answer we got by the other method.
.
Maybe these two ways of looking at the problem will help you see your way through it.
.
Hope this helps ...
.
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