One night Bran had a dream in which he grew a constant amount each hou

Solution:

• The original height of Mark =\( 3\frac{ 3}{4}=15/4\) feet
• Mark’s height is increasing at a constant rate each hour.

o Let \(x\) be the increase in height of mark each hour.
• Now, the question says at the end of the third hour Mark’s height is \(\frac{1}{4}\)th less than his height at the end of nine-hour.

Note:-The question states \(\frac{1}{4}\) less not \(\frac{1}{4}\) feet less
o Mark’s height at the end of the third hour = \(\frac{15}{4} + 3*x\)
o Marks' height at the end of nine-hour = \(\frac{15}{4} + 9*x\)

 According to the condition given.
\(\frac{15}{4}+3*x=(1-\frac{1}{4}) (\frac{15}{4}+9*x)\)
\(15+12*x=\frac{(45+108*x)}{4} \)
\(60+48*x=45+108*x \)
\(108*x-48*x=60-45\)
\(60*x=15 \)
\(x=\frac{15}{60}=\frac{1}{4}\) feet

• Now, the height of mark at the end of the seventh hour = \(\frac{15}{4}+7*x=\frac{15}{4}+7*\frac{1}{4}=\frac{22}{4}=\frac{11}{2}=5\frac{ 1}{2}\) feet.