How many tracks are there? How long is each track? How much space does one car occupy on a track?
B
b
Simplify the expression found in Part A.
C
c
Write an expression that represents the time needed for a safety check of one car.
A
a
5tracks *2miles/1track*5280feet/1mile*1car/75feet
B
b
704 cars
C
c
70.4 hours
Practice makes perfect
a
We want to write an expression that could be used to determine the number of train cars involved in the backup. Let's point out what we already know.
There are 5 tracks.
Each track is 2 miles long.
One car occupies an average of 75 feet of space on a track.
Note that the length of the track is expressed in miles, meanwhile the space occupied by one car is expressed in feet. Therefore, we will have to change the unit. Recall that 1mile is equal to 5280feet. Let's start writing the expression.
There are 5tracks. Each track is 2 miles long.
5tracks *2miles/1track*...
Now we will change the unit.
5tracks *2miles/1track*5280feet/1mile*...
Finally, we will use the last given information and finish our expression.
One car occupies an average of 75feet
of space on a track.
5tracks *2miles/1track*5280feet/1mile*1car/75feet
b
To determine how many train cars are involved in the backup, we will simplify the expression found in Part A.
First, we will write an expression that represents the time needed for a safety check of one car. Let's point out what we already know.
There are 8 attendands doing a safety check on each car.
One check done by one attendant takes on average 45 seconds.
Now, we will write our expression.
8attendants/1car*45s/1attendant
Note that we are asked to give the answer in hours. Let's change the unit from seconds to hours. There is 60 seconds in 1 minute and 60 minutes in 1 hour.
8attendants/1car*45s/1attendant*1min/60s*1h/60min
We have obtained an expression that represents the time needed for a safety check of one car. From Part B we know that there are 704 cars involved in the backup.
704cars*8attendants/1car*45s/1attendant*1min/60s*1h/60min
Finally, we will simplify this expression.
