# Word Problems/Proportions

Question
QUESTION: Hello:

If a automobile travels 200 miles in 5 hours, how many miles will it travel in 1 hour?

I used this proportion to determine the answer:

200 miles /? miles = 5 hours/1 hour

? = 40 miles

My question is as follows:  Is it correct to express this proportion as 200 miles is to 40 miles as 5 hours is to 1 hour?

Are these correct?
200 miles is to 5 hours as 40 miles is to 1 hour?

200 miles is to 1 hour as 5 hours is to 40 miles?

There are more combinations, but I just wanted to know whether or not the same units need to be matched with the other units of the same kind in the proportion, miles with miles and hours with hours.

It could also be done as 200/5 = x/1.

Since x/1 = x, we have x = 200/5 = 40.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for the reply.

What does a is to b as c is to d indicate regarding proportions?

In my example, 200 miles is to 40 miles as 5 hours is to 1 hour indicates what?

The key is to make sure the units on both side are the same.

It could be a=200, b=40, c=5, and d is unknown.
This would be miles/miles = hours/hours.
It would say that a/b = c/d, so 200/40 = 5/d.
Since 200/40 is 5, so we have 5 = 5/d, sowe have d=1.

It could be a=40, b=200, d=5, and c is unknown.
This would be the same units as the last, miles/miles = hours/hours.
It would say that 40/200 = c/5.
Here, 40/200 = 1/5, so 1/5 = c/5, so c=1.

It could be a=200, b=5, c=40, and d is unknown.
This would be miles/hours = miles/hour.
It would say that 200/5 = 40/d.
Since 200/5 = 40, we have 40 = 40/d, so d=1.

Word Problems

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#### Scott A Wilson

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