Question

A turtle moves ‘i’ inches in ‘m’ minutes. At the rate, how many feet can it move in an hour?
(a) $\dfrac{5hi}{m}$
(b) $\dfrac{60hi}{m}$
 (c) $\dfrac{hi}{12m}$
 (d) $\dfrac{5m}{hi}$

Answer 1

Hint: Firstly, we will use the conversion formulas for feet to inches and hours to minutes as 1 feet= 12 inches and 1 hour= 60 minutes. Then, we have to consider the distance as x in feet per hour. Then, by using proportion and substituting the values of the x feet and h hours in corresponding inches and minutes values respectively to get the final relation.

Complete step by step answer:
In this question, we are supposed to find the rate of the speed of the turtle in feet per hour but the problem is that it is given in inches per minute.
So, we need to convert the inches per minute to feet per hour.
Now, by using the condition given in the question that the turtle moves ‘i’ inches in ‘m’ minutes.
We are asked to find how many feet it will take to move in h hours.
Here, we need to convert feet into inches and hours into minutes.
Now, by using the relations as:
1 feet= 12 inches
1 hour= 60 minutes
Let us suppose the distance travelled by the turtle is x in feet per hour.
So, convert x feet into inches by using the above conversion formula as:
x feet= 12x inches
Now, similarly we can convert h hours to minutes by using the conversion stated above as:
h hours= 60h minutes
Now, to get the distance travelled by the turtle in feet per hour, we need to form a proportion which states that distance travelled by turtle in inches per minutes is equal to the distance travelled by the turtle in corresponding feet per hour value.
So, to get them in proportion we have:
$\dfrac{i}{m}=\dfrac{12x}{60h}$
Solve the above proportion for the value of x to get the distance travelled by the turtle in feet per hours as:
So, by cross multiplying the above equation for value of x as:
$\begin{align}
  & x=\dfrac{60hi}{12m} \\
 & \Rightarrow x=\dfrac{5hi}{m} \\
\end{align}$
So, the turtle walks with the speed of $\dfrac{5hi}{m}$in feet per hour.
Hence, option (a) is correct.

Note: For doing these kinds of questions, the only mistake we may make is taking the wrong values of the conversion or there is also a possibility that even we don’t know the conversion. So, to get the correct answer in these types of questions we must be aware of the simple conversions such as from km to m, l to ml, feet to inch, feet to metre, hours to minutes, minutes to seconds, etc. So, the conversions required for this question are as follows:
1 feet= 12 inches
1 hour= 60 minutes.