Sakura speaks 150 words per minute on average in Hungarian a

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? Sakura spoke for minutes in Hungarian and for minutes in Polish.

Solution

Let us assume that Sakura spoke for x minutes in Hungarian. Then, she spoke for 5-x minutes in Polish ( as she spoke in these 2 languages for a total of 5 minutes).Then the words in Hungarian and Polish spoken by Sakura were 150x and 190(5-x) respectively. Further, since Sakura spoke 270 more words in Polish than in Hungarian, hence 190(5-x) = 150x +270 or, 950-190x = 150x +270 or, 190x+150x = 950-270 or, 340x = 680 so that x = 680/340 = 2. Then 5 – x = 5-2 = 3. Thus, Sakura spoke for 2 minutes in Hungarian and 3 minutes in Polish.