Given the height of tree is 3 feet tall
Let [tex] h_{1} [/tex] be the height of 3 feet tall tree which is growing at the rate of 1 foot per year.
Let the rate at which tree is growing be 't'.
[tex] h_{1} = 3+( 1 \times t) [/tex] = 3+ t
Given the height of tree is 5 foot.
Let [tex] h_{2} [/tex] be the height of 5 foot tall tree which is growing at the rate of 0.75 foot per year.
[tex] h_{2} = 5+( 0.75 \times t) [/tex] = 5+0.75t
We have to find the the number of years elapsed when the trees are at the same height.
Therefore, [tex] h_{1}=h_{2} [/tex]
[tex] 3+t = 5+0.75t [/tex]
[tex] 3-5 = 0.75t-t [/tex]
[tex] -2=-0.25t [/tex]
t = 8.
Therefore,
As [tex] h_{1}=3+t [/tex]
[tex] h_{1}=3+8 [/tex]
[tex] h_{1}= 11 [/tex]
Therefore, (8,11) represents the number of years elapsed when the trees are at the same height.
