Question

How many minutes does it take John to type “\[y\]” words if he types at the rate of “\[x\]” words per minute?
A. \[\dfrac{x}{y}\]
B. \[\dfrac{y}{x}\]
C. \[xy\]
D. \[\dfrac{{60x}}{y}\]
E. \[\dfrac{y}{{60x}}\]

Answer 1

Hint: First find that how much time it takes John to type \[1\] word and then find the time taken to type \[y\] number of words. Use the concept of multiplication by first finding how much time is need to type the words in 1 minute.

Complete Step-by-step Solution
Given: John type at the rate of “\[x\]” words per minute.
To find: We have to find the total time it takes John to type “\[y\]” words.
As it is given that the “\[x\]” number of words John type in \[1\] minute.
Number of words John type in \[1\] minute \[ = x\].
Hence, “\[y\]” number of words John type in \[\dfrac{y}{x}\] minutes.
So, it takes \[\dfrac{y}{x}\] minutes.
It takes John to type “\[y\]” words if he types at the rate of “\[x\]” words per minute.

Hence the correct option is B.

Note:
In such type of problems, write the number of words in numerator and rate per minute to type a word in the denominator.
For example, if a person types at the rate of \[30\] words per minute, then how many minutes does it take a person to type \[60\] words.
Here \[y\] is 60 and \[x\] is 30.
Number of words a person type in \[1\] minute \[ = \dfrac{1}{{30}}\] minutes.
A person will type \[1\] Word in \[ = \dfrac{1}{{30}}\] minutes
As, “\[y\]” number of words a person type in \[\dfrac{y}{x}\] minutes.
Use 60 for \[y\] and 30 for \[x\] in \[\dfrac{y}{x}\].
Then, A person will type \[60\] words in \[ = \dfrac{{60}}{{30}}\]
On simplifying \[\dfrac{{60}}{{30}} = 2\]
Thus, A person will type \[60\] words in \[2\] Minutes.