During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During this time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel?
A. 36
B. 37.5
C. 40
D. 80
E. 90
I am quite confused in this problem, can some experts help me?
OA E
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Since 5 gallons are used every 2 hours, 2 hours is the equivalent of 5 gallons.lheiannie07 wrote:During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During this time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel?
A. 36
B. 37.5
C. 40
D. 80
E. 90
Since there are 60 minutes in an hour, 60 minutes is the equivalent of 1 hour.
Since the rate is 1 mile per minute, 1 mile is the equivalent of 1 minute.
Use the ratios above to convert the amount of gas used -- 15/4 gallons -- to miles.
(15/4 gallons) * (2 hours/5 gallons) * (60 minutes)/(1 hour) * (1 mile)/(1 minute).
In the expression above, all of the colored values CANCEL OUT, leaving the calculation in terms of MILES.
Calculating the value of the expression above, we get:
(15/4) * (2/5) * (60/1) * (1/1) = 90 miles.
The correct answer is E.
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We can also calculate step-by step.lheiannie07 wrote:During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During this time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel?
A. 36
B. 37.5
C. 40
D. 80
E. 90
Since the rate is 5 gallons per 2 hours, and the total gas used = 3.75 gallons, we can set up the following proportion:
(5 gallons)/(2 hours) = (3.75 gallons)/(x hours).
5x = (2)(3.75)
5x = 7.5
x = 1.5 hours.
1.5 hours = 90 minutes.
Since the car traveled for 90 minutes at a rate of 1 mile per minute, the distance traveled = rt = 1*90 = 90 miles.
The correct answer is E.
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BTGmoderatorDC wrote:During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During this time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel?
A. 36
B. 37.5
C. 40
D. 80
E. 90
Since the car has a constant rate of 1 mile per minute, we can let x = the rate of the car in miles per hour and create the following proportion:
1/1 = x/60
x = 60 mph
Since the car uses 5 gallons of fuel every 2 hours, we can let x = the number of hours driven when the car uses 3.75 gallons of fuel and create the following proportion:
5/2 = 3.75/x
5x = 7.5
x = 1.5 hours
We know that the rate of the car is 60 mph and the car has been driven for 1.5 hours; thus, the distance driven is 60 x 1.5 = 90 miles.
Alternate Solution:
Since the car uses 5 gallons of fuel every 2 hours, or 120 minutes, we can let x = the number of minutes for which the car uses 3.75 gallons of fuel and create the following proportion:
5/120 = 3.75/x
5x = 120(3.75)
x = 90
So, the car is driven for 90 minutes. Since it travels 1 mile per minute, it will have traveled 90 miles.
Answer: E
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