Question

Rita types 2070 words in 3/2
h. How long will she take to type 3450 words? How many words will she type in 3 hours?

Answer 1

Given,

• Words typed in 3/2 hrs = 2070

¤ To find :-

• Time taken to type 3450 words
• Words typed in 3 hours

Here,

Words typed in 3/2 hrs = 2070

$\to \text{Words typed in 1 hrs = } \frac{2070}{ \frac{3}{2} } \\ \: \: \: \: \: \: \: \implies \frac{2070 \times 2}{3} \\ \: \: \: \: \: \: \: \implies 690 \times 2 \: \: \to \green{1380}$

• 1380 word are typed in 1 hour.

$\text{Time taken to type 2070 words = } \bf \frac{3}{2} \: hrs \\ \\ \therefore \: \text{Time taken to type 1 word = } \frac{ \frac{3}{2} }{2070} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \: \: \: \frac{3}{2 \times 2070} = \frac{ \cancel3}{2 \times \cancel3 \times 690} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \: \: \: \frac{1}{2 \times 690} = \bf \frac{1}{1380} \: \: hrs$

Now,

$\boxed{ \small\bullet \: \: \text{Time taken to type 3450 words} = \pink{3450 \times \text{Time taken to type 1 word}} }\\ \: \: \: \: \: \: \: \: \: \: \implies3450 \times \frac{1}{1380} \\ \: \: \: \: \: \: \: \: \: \: \implies \frac{345 \cancel0}{138 \cancel0} \: \: \to \bf \red{2.5} \: hrs$

And,

$\boxed{ \small\bullet \: \: \text{Words typed in 3 hours} = \pink{3 \times \text{Words are typed in 1 hour}}} \\ \bf \: \: \: \: \: \: \: \implies3 \times 1380 \\ \bf \: \: \: \: \: \: \: \implies \red{4140}$

Hence,

• 2.5 hours are taken for typing 3450 words.
• 4140 words are typed in 3 hours.

Answer 2

Step-by-step explanation:

Given,

Words typed in 3/2 hrs = 2070

¤ To find :-

Time taken to type 3450 words

Words typed in 3 hours

Here,

Words typed in 3/2 hrs = 2070

\begin{gathered} \to \text{Words typed in 1 hrs = } \frac{2070}{ \frac{3}{2} } \\ \: \: \: \: \: \: \: \implies \frac{2070 \times 2}{3} \\ \: \: \: \: \: \: \: \implies 690 \times 2 \: \: \to \green{1380}\end{gathered}→Words typed in 1 hrs = 232070⟹32070×2⟹690×2→1380

1380 word are typed in 1 hour.

\begin{gathered}\text{Time taken to type 2070 words = } \bf \frac{3}{2} \: hrs \\ \\ \therefore \: \text{Time taken to type 1 word = } \frac{ \frac{3}{2} }{2070} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \: \: \: \frac{3}{2 \times 2070} = \frac{ \cancel3}{2 \times \cancel3 \times 690} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \: \: \: \: \frac{1}{2 \times 690} = \bf \frac{1}{1380} \: \: hrs\end{gathered}Time taken to type 2070 words = 23hrs∴Time taken to type 1 word = 207023⟹2×20703=2×3×6903⟹2×6901=13801hrs

Now,

\begin{gathered}\boxed{ \small\bullet \: \: \text{Time taken to type 3450 words} = \pink{3450 \times \text{Time taken to type 1 word}} }\\ \: \: \: \: \: \: \: \: \: \: \implies3450 \times \frac{1}{1380} \\ \: \: \: \: \: \: \: \: \: \: \implies \frac{345 \cancel0}{138 \cancel0} \: \: \to \bf \red{2.5} \: hrs\end{gathered}∙Time taken to type 3450 words=3450×Time taken to type 1 word⟹3450×13801⟹13803450→2.5hrs

And,

\begin{gathered}\boxed{ \small\bullet \: \: \text{Words typed in 3 hours} = \pink{3 \times \text{Words are typed in 1 hour}}} \\ \bf \: \: \: \: \: \: \: \implies3 \times 1380 \\ \bf \: \: \: \: \: \: \: \implies \red{4140}\end{gathered}∙Words typed in 3 hours=3×Words are typed in 1 hour⟹3×1380⟹4140

Hence,

2.5 hours are taken for typing 3450 words.

4140 words are typed in 3 hours