Question

Sakura speaks 150 words per minute on average in Hungarian, and 190 words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent 5 minutes total giving both instructions, and spoke 270 more words in Polish than in Hungarian. How long did Sakura speak in Hungarian, and how long did she speak in Polish?

Answer 1

Sakura spoke Polish for 3 minutes.

Step-by-step explanation:

Let Sakura speaks Hungarian H words

She spoke 270 more words in polish than Hungarian so

she spoke Polish (H+270)words.

she spoke 150 Hungarian words in 1 min, so for H words, H/150 Min,

190 Polish words in 1 min, so for H+270 words, H+270/190 min.

In total Sakura spoke for 5 min, H/150 + (H +270)/190 =5

solving this eq ,we get 19H +15H +270*15 = 50*15*19

34H = 50*15*19 - 270*15

34H = 150(95-27)

34H =150*68

H =150*68/34 = 300, She spoke 300 Hungarian words,300/150=2 it would take 2 min, she spoke H+270= 300+270= 570 Polish words..

it would take 570/190= 3 min

Answer 2

Taking into account the information in the exercise, Sakura spoke Hungarian for:

• 2 minutes.

And Polish:

• 3 minutes.

Step-by-step explanation:

To solve the exercise, variables must be generated both for the time that Hungarian Sakura spoke and for the time that Polish spoke:

• Words Sakura spoke Polish: P
• Words Sakura spoke Hungarian: H

To identify the time she was speaking in each language, the exercise information must be taken into account, that is, Sakura speaks 150 words in Hungarian per minute and 190 words in Polish per minute, such information must be expressed as formulas by adding the variables already created:

• Time Sakura spoke Polish in minutes= X = P/190
• Time Sakura spoke Hungarian in minutes= Y= H/150

As the only additional information was that he spent 5 minutes speaking and used 270 more words in Polish than in Hungarian, everything is expressed within a compound equation:

• 5 minutes= X+Y
• 5 minutes= (P/190)+(H/150)

And everything must be expressed based on a single variable, either H or P, in this case the variable P will be chosen:

• 5 minutes= (P/190)+((P-270)/150). "(P-270) is used because it is the number of extra words spoken in Polish"

The sum of fractionals is done:

• 5 minutes= (150P + 190P - 51300)/28500

Terms of the same type are located next to the equation:

• (5*28500)+51300= 190P + 150P
• 193800= 340P
• 193800/340=P
• P= 570 words

The value obtained is replaced in the time formula:

• X= 570/190
• X= 3 minutes

And the general formula is replaced:

• 5 minutes= X + Y
• 5 minutes= 3 minutes + Y
• 5 minutes - 3 minutes= Y
• Y= 2 minutes

To check the number of words, you can multiply the time in minutes by the number of words:

• H =2*150
• H= 300 words

And 570 words in Polish, there are 270 more than 300 words in Hungarian.