# If Sam types at a rate $x$ words per minute, calculate how many minutes, in terms of $x$, will it take him to type 500 words.

A.$500x$

B.$500-x$

C.$500+x$

D.$\dfrac{500}{x}$

E.$\dfrac{x}{500}$

Last updated date: 23rd Mar 2023

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Answer

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Hint: At first find out the value of a unit. That means how many minutes will it take Sam to type one word. Then calculate how many minutes it will take him to type 500 words.

It is given in the question that Sam types at a rate $x$ words per minute.

If he can type $x$ words in one minute, then to type one word he will take less than one minute.

We can solve this problem using a unitary method in which we find the value of a unit and then value of a required number of units.

Always write the things to be found on the right hand side and things known on the left hand side.

In the above problem we need to find out the time. That means we will take time on the right hand side.

We know the number of words, so words are the known thing here. That means we will take words on the left hand side.

First we need to find out the value of a unit. Here unit means one word. Then the value of the required number of words, that means 500 words.

Sam types $x$ words in 1 minute.

Sam types 1 word in $\dfrac{1}{x}$ minute. Here we are dividing because if Sam can type $x$ words in one minute, he will take less time to type just one word.

Sam types 500 words in $\dfrac{1}{x}\times 500$ minutes.

Therefore, Sam types 500 words in $\dfrac{500}{x}$ minutes.

Hence, option (d) is correct.

Note: We generally make mistakes when we calculate the value of a unit. We need to understand by reading the question that the value of a unit is increasing or decreasing. If it is decreasing then we have to divide and if it is increasing then we have to multiply.

__Complete step-by-step answer:__It is given in the question that Sam types at a rate $x$ words per minute.

If he can type $x$ words in one minute, then to type one word he will take less than one minute.

We can solve this problem using a unitary method in which we find the value of a unit and then value of a required number of units.

Always write the things to be found on the right hand side and things known on the left hand side.

In the above problem we need to find out the time. That means we will take time on the right hand side.

We know the number of words, so words are the known thing here. That means we will take words on the left hand side.

First we need to find out the value of a unit. Here unit means one word. Then the value of the required number of words, that means 500 words.

Sam types $x$ words in 1 minute.

Sam types 1 word in $\dfrac{1}{x}$ minute. Here we are dividing because if Sam can type $x$ words in one minute, he will take less time to type just one word.

Sam types 500 words in $\dfrac{1}{x}\times 500$ minutes.

Therefore, Sam types 500 words in $\dfrac{500}{x}$ minutes.

Hence, option (d) is correct.

Note: We generally make mistakes when we calculate the value of a unit. We need to understand by reading the question that the value of a unit is increasing or decreasing. If it is decreasing then we have to divide and if it is increasing then we have to multiply.

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