tebollahb

2021-12-26

If it takes 42 minutes to load $3\frac{1}{2}$ trucks, how many minutes will it take to load $6\frac{1}{2}$ trucks?

karton

We know that it takes 42m to load $3\frac{1}{2}$ trucks.
We want to find out how long it takes to load $6\frac{1}{2}$ trucks.
Too bad it was not the time wanted to load 7 trucks, because:
7 trucks $=2\left(3\frac{1}{2}\right)$ trucks so the answer would be:
2(42m)=84m for 7 trucks.
The reason we should bother with this answer is because:
Now we have an estimate for the real answer we will need to find (must be slightly less than 84m).
We could find the time it takes to load 1 truck by dividing the time (42m) by $3\frac{1}{2}$ and $3\frac{1}{2}=\frac{6+1}{2}=\frac{7}{2}$
$\frac{42m}{\frac{7}{2}}=42×\frac{2}{7}=\frac{84m}{7}=12m\to$ after invert and multiply.
Then we could multiply the time to load 1 truck by $6\frac{1}{2}$ as asked:
$12m×6\frac{1}{2}=72m+\frac{1}{2}\left(12m\right)=72m+6m=78m$
And that is in line with our estimate of 84m calculated previously.

user_27qwe

Explanation:
The more trucks, the more minutes.
$\frac{42}{x}=\frac{3.5}{6.5}\to x=42\cdot \frac{65}{35}=6\cdot 13$

nick1337

Given that 42 minutes are required to load $3\frac{1}{2}$ trucks.
Let ‘x minutes’ be the time to load $6\frac{1}{2}$ trucks.
$3\frac{1}{2}$ trucks $\to$ 42 minutes
$6\frac{1}{2}$trucks $\to x$
By cross multiplication
$\begin{array}{}3\frac{1}{2}×x=6\frac{1}{2}×42\\ x=\left(6\frac{1}{2}×42\right)/3\frac{1}{2}\\ =\frac{\left(\frac{13}{2}×42\right)}{\frac{7}{2}}\\ x=78\end{array}$
Thus x=78 minutes

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