Question

A machine can paint 340 toy boats in 45 minutes. How many boats can it paint in one hour?

Answer 1

Hint: We will first convert the 45 minutes into hours. Then, we will use the unitary method to find out how many toys can be painted in an hour with the same rate.

Complete step by step answer:
We are given that we are required to find out how many toys can be painted in an hour, when 340 toys can be painted in 45 minutes.
We know that in 1 hour, we have 60 minutes.
This can be written as follows:-
60 minutes equals 1 hour.
Therefore, 1 minute is equal to $\dfrac{1}{{60}}$ hrs.
Now, multiplying this by 45 in the minute’s side as well as the hour side, we will then obtain the following equation with us:-
Therefore, 45 minutes are equal to $\dfrac{{45}}{{60}}$ hrs.
Crossing – off 15 from both the numerator and denominator, we will then obtain the following equation with us:-
Thus, we have: 45 minutes are equal to \[\dfrac{3}{4}\] hrs.
Thus, we have: In \[\dfrac{3}{4}\] hours, we have painted 340 toy boats.
Therefore, in 1 hour, we can paint $\dfrac{{340}}{{\dfrac{3}{4}}}$ toy boats.
Therefore, In 1 hour, we can paint $\dfrac{{340 \times 4}}{3} = \dfrac{{1360}}{3}$ toy boats.
Thus, we have 453.33 toy boats per hour.

Note:
The students must note that we have crossed – off 15 from both the numerator and denominator because we know that 15 can never be equal to 0 and we can never cross – off any variable which has even the slightest possibility of being equal to 0.
The students must also commit to the memory that: 60 minutes equals to 1 hour.
The students must go to find out about 1 unit when some other unit is given that is known as the unitary method. Here, we have used the unitary method only in the solution mentioned above.