Mark B. answered • 03/30/18
Tutor
New to Wyzant
PhD Candidate and Math Tutor with 20 Years of Experience: All levels.
Hello Zain,
Your word problem can be easily set up as a proportional problem. Why? If you look at the problem, you are given three factors or variables.
Those factors are as follows:
You know that the car is traveling 60km PER hour. These are the first two factors, and whenever you see PER in a problem you can usually bet that you can make that a ratio, or fraction.
That part of your problem is expressed as follows: 60km/1 hour. Notice the fraction I just provided is the exact same as 60km per hour. We good so far?
But then, you are provided an additional piece of information, right? And what is that additional piece tell, or ask. How long does it take for the same car to travel 45km? The only part missing is the time it takes to travel that distance. Do you see it?
When setting up proportions, you want to set two fractions or ratios equal to each other. The way to best accomplish this is by placing like LIKE units of measure on each numerator and denominator of your ratio. In your problem, for example:
60 km 45 km
------- = --------
1 x
When looking at this proportional equation you can quickly see the left ratio indicates the first part of the problem as stated originally, and the second ratio on the right gives you the distance but not the time. It could be expressed verbally as 45km in x hours?
Now, all you need do is cross multiply the terms in order to begin solving. You take the numerator on the left and multiply it by the denominator on the right. Placing the equal sign to the right side now, we take the denominator on the left and multiply it by the numerator on the right. This leads to the following equation:
60km (x) = 45km Solve for x now. Divide both sides of the equation by 60km leaving x to itself.
Therefore:
x = 45km/60km Now reduce the ratio or fraction. When looking at this fraction you can see both the numerator and denominator can be reduced by dividing each by 15, right? Doing so leaves you with 3km/4km and you want to remember you are looking for the time it takes for your answer.
Since the answer is 3km/4km of an hour, we now can determine that it takes 3/4 of an hour to travel the 45 kilometers.
3/4 of an hour is the same as 45 minutes, right? Therefore:
Your answer is it will take 45 minutes for that car to travel that particular distance.
Please note: I could have easily given you the answer through a short-cut however I feel an obligation to exercise due diligence as a tutor to provide you the reason why you use a proportional equation and how to do so. Later down the road, be certain you will need to know how to do proportions in order to solve more complex problems whether in chemistry, physics or any number of subjects, okay?
Again, your answer is 45 minutes to travel 45 Kilometers. Does this make sense? Please let me know in the comment section below.
I hope I have helped you and wish you a Happy Easter Holiday weekend.
Your word problem can be easily set up as a proportional problem. Why? If you look at the problem, you are given three factors or variables.
Those factors are as follows:
You know that the car is traveling 60km PER hour. These are the first two factors, and whenever you see PER in a problem you can usually bet that you can make that a ratio, or fraction.
That part of your problem is expressed as follows: 60km/1 hour. Notice the fraction I just provided is the exact same as 60km per hour. We good so far?
But then, you are provided an additional piece of information, right? And what is that additional piece tell, or ask. How long does it take for the same car to travel 45km? The only part missing is the time it takes to travel that distance. Do you see it?
When setting up proportions, you want to set two fractions or ratios equal to each other. The way to best accomplish this is by placing like LIKE units of measure on each numerator and denominator of your ratio. In your problem, for example:
60 km 45 km
------- = --------
1 x
When looking at this proportional equation you can quickly see the left ratio indicates the first part of the problem as stated originally, and the second ratio on the right gives you the distance but not the time. It could be expressed verbally as 45km in x hours?
Now, all you need do is cross multiply the terms in order to begin solving. You take the numerator on the left and multiply it by the denominator on the right. Placing the equal sign to the right side now, we take the denominator on the left and multiply it by the numerator on the right. This leads to the following equation:
60km (x) = 45km Solve for x now. Divide both sides of the equation by 60km leaving x to itself.
Therefore:
x = 45km/60km Now reduce the ratio or fraction. When looking at this fraction you can see both the numerator and denominator can be reduced by dividing each by 15, right? Doing so leaves you with 3km/4km and you want to remember you are looking for the time it takes for your answer.
Since the answer is 3km/4km of an hour, we now can determine that it takes 3/4 of an hour to travel the 45 kilometers.
3/4 of an hour is the same as 45 minutes, right? Therefore:
Your answer is it will take 45 minutes for that car to travel that particular distance.
Please note: I could have easily given you the answer through a short-cut however I feel an obligation to exercise due diligence as a tutor to provide you the reason why you use a proportional equation and how to do so. Later down the road, be certain you will need to know how to do proportions in order to solve more complex problems whether in chemistry, physics or any number of subjects, okay?
Again, your answer is 45 minutes to travel 45 Kilometers. Does this make sense? Please let me know in the comment section below.
I hope I have helped you and wish you a Happy Easter Holiday weekend.
Best,
