Question

Two grapes vines are growing in Runa's backyard. She bought the first vine when it was $11$ inches long. Its growth rate was $0.25$ inches per day. After $20$ days, Runa bought the second vine, which started at $24$ inches long . It has a growth rate of $0.125$ inches per day. How many days will Runa have had the first vine when the lengths of the two vines are the same?

Answer 1

Given that Runa bought first vine when $20$ inch long and its growing rate is $0.25$ inches per day

And he bought second vine after $20$ day which $24$ inches long and its growth rate $0.125$ inches per day

Len after $20$ days both vine are equal length in after $x$ day

Then length of first vine after $(20+x)=$ $0.25\times (20+x)+11$

And length of second vine after $x$ day $=$ $0.125\times x+24$

Then these are equal, when

$0.25\times (20+x)+11=0.125\times x+24$

$\Rightarrow 5+0.25x+11=0.125x+24$

$\Rightarrow 0.25x-0.125x=24-11-5$

$\Rightarrow 0.125x=8$

$\Rightarrow x=64$

Then length of two vine are same in days $=64+20=84$ days