Question

Sakura speaks 150150 words per minute on average in Hungarian, and 190190 words per minute on average in Polish. She once gave cooking instructions in Hungarian, followed by cleaning instructions in Polish. Sakura spent 55 minutes total giving both instructions, and spoke 270270 more words in Polish than in Hungarian. How long did Sakura speak in Hungarian, and how long did she speak in Polish? Sakura spoke for minutes in Hungarian and for minutes in Polish.

Answer 1

Sakura spoke for 2 minutes in Hungarian and for 3 minutes in Polish.

Explanation:

Let H represent the number of minutes Sakura spoke in Hungarian and P represent the number of minutes Sakura spoke in Polish.

We have been given that Sakura speaks 150 words per minute on average in Hungarian, so total Hungarian words spoken in H minutes will be 150H.

Sakura also speaks 190 words per minute on average in Polish, so total Polish words spoken in P minutes will be 190P.

Sakura spoke 270 more words in Polish than in Hungarian. We can represent this information in an equation as:

`190P-150H=270...(1)`

Sakura spent 5 minutes total giving both instructions. We can represent this information in an equation as:

`H+P=5...(2)`

We will use substitution method to solve our system of linear equations.

From equation (2) we will get,

`H=5-P`

Upon substituting this value from equation (1) we will get,

`190P-150(5-P)=270`

`190P-750+150P=270`

`190P-750+750+150P=270+750`

`190P+150P=270+750`

`340P=1020`

`(340P)/(340)=(1020)/(340)`

`P=3`

Therefore, Sakura spoke for 3 minutes in Polish.

Let us substitute P=3 in equation (2) to solve for H.

`H+3=5`

`H+3-3=5-3`

`H=2`

Therefore, Sakura spoke for 2 minutes in Hungarian.