Answer:
9 years
Explanation:
Let the the number of years in which height of both the type of tree is same be n years
Initial length of type A tree = 7 feet
As rate of growth is given in inches to maintain uniformity of measuring unit lets convert feet to inches
1 feet = 12 inches
thus 7 feet = 12*7 inches = 84 inches.
length of type A tree in inches = 84 inches
Rate of growth of type A tree = 10 inches per year
Thus, actual growth of type a tree in "n" years = 10*n = 10n
Total height of type A tree in n years = initial length + growth in n years
= 84 inches+ 10n inches (1)
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For type B
Initial length of type B tree = 4 feet
As rate of growth is given in inches to maintain uniformity of measuring unit lets convert feet to inches
1 feet = 12 inches
thus 4 feet = 12*4 inches = 48 inches.
length of type B tree in inches = 48 inches
Rate of growth of type A tree = 14 inches per year
Thus, actual growth of type a tree in "n" years = 14*n = 14n
Total height of type b tree in n years = initial length + growth in n years
= 48 inches+ 14n inches (2)
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Given condition that after n years height of both the type of tree is same
equation 1 should be equal to equation 2
84 inches+ 10n inches = 48 inches+ 14n inches
=>84 inches - 48 inches = 14n inches - 10n inches
=> 36 inches = 4n inches
=> 36 = 4n
=> n = 36/4 = 9
Thus, after 9 years both of their height will be same which be equal to
84+10*9 = 84 + 90 = 174 inches.