Question

Convert 180 minutes to an hour.

Answer 1

Hint: We recall the working of the clock, the hour and minute hand. We recall how many minutes make 1 hour. We use it for direction variation in the unitary method and divide 180 by 60 to get the converted answer.

Complete step-by-step solution

We know that in a watch the 12 numbers from 1 to 12 to represent the measurement of time. The hour hand is the shortest hand in the watch which moves from one number to another to represent the passing one hour. The minute hand is the long hand which moves from one digit to another to represent the passing of 5 minutes. So when minute hands pass all the 12 numbers it will take a total of $12\times 5=60$ minutes and by that time the hour hand would have moved only to the next number. It means it 1hour is equal to 60 minutes. We are asked in the question to convert 180 minutes to hours. We shall use unitary with direction variation where one quantity $a$ increases with another quantity $b$ and also $a$ decreases with $b$ then we say the quantities $a$ and $b$ are in direct variation. \[\]
Here is the number of minutes increases the number of hours also increases, so the problem is in direct variation. We have already obtained the value of a single unit that is the number of minutes in 1 hour that is 60 minutes. So we divide 180 minutes by 60 to have the required numbers of hours as $\dfrac{180}{60}=3$ \[\]

Note: We know that the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying or dividing with the single unit value. If the number of minutes is not multiple of 60 we are going to get the number of hours in decimals. The third hand of the clock is called second hand and 60 seconds makes 1 minute.