A long session lasts 50 minutes.
Step-by-step explanation:
Let,
Duration of long session = x
Duration of short session = y
According to given statement;
3x+4y=270 Eqn 1
each long session lasts twenty minutes longer than the short session.
x = y + 20 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]3(y+20)+4y=270\\3y+60+4y=270\\7y=270-60\\7y=210[/tex]
Dividing both sides by 7
[tex]\frac{7y}{7}=\frac{210}{7}\\y=30[/tex]
Putting y = 30 in Eqn 2
[tex]x=30+20\\x=50[/tex]
A long session lasts 50 minutes.
Keywords: linear equation, substitution method
Learn more about substitution method at:
#LearnwithBrainly
Time taken by long session is 50 minutes
Given that;
Total time taken for all session = 270 minutes
Number of long session = 3
Number of short session = 4
Assume;
Time taken by short session = a
Time taken by long session = a + 20
So,
3[a + 20] + 4[a] = 270
3a + 60 + 4a = 270
7a + 60 = 270
7a = 210
a = 30 minutes
Time taken by long session = a + 20
Time taken by long session = 30 + 20
Time taken by long session = 50 minutes
Learn more:
https://brainly.com/question/8806520?referrer=searchResults
