Answer:
To consume n liters of water , it takes 1.5n hours.
It takes 9 hours to drink all the water.
Step-by-step explanation:
Given - You start your day at school with a full bottle of water, which
contains 6 liters of water. You drink 2 liters of water every
3 hours.
To find - Make a web that represents this situation. How many hours
does it take you to drink all the water?
Proof -
Given that,
Total litres of water = 6 litres
Also,
He drinks 2 litres of water = 3 hours
⇒ 1 litre of water = [tex]\frac{3}{2}[/tex] hours
⇒6 litres of water = [tex]\frac{3}{2}.6[/tex] = [tex]\frac{18}{2}[/tex] = 9 hours
∴ we get
It takes 9 hours to drink all the water.
For the web -
We can see that
For 1 litres it takes 1.5 hours
For 2 litres it takes 3 hours
For 3 litres it takes 4.5 hours
For 4 litres it takes 6 hours
We can see it is becoming an Arithmetic Progression (A.P) with common difference 1.5 and starting with 1.5
So, a₁ = 1.5 , d = 1.5
aₙ be n litres of water at a time.
We know A.P is - aₙ = a₁ + (n - 1)d
⇒aₙ = 1.5 + (n-1)1.5
⇒aₙ = 1.5 + 1.5n - 1.5
⇒aₙ = 1.5n
∴ we get
To consume n liters of water , it takes 1.5n hours.
