Emily rode x miles, from her home, at a speed of p miles per hour befo

Solution

• Let us assume that Emily walked her motorcycle for w miles.
• So, the distance traveled(in miles) by Emily in the first half of the journey \( = x + w\)

o Thus, total time taken(in hours) by Emily to cover the first half of the journey \(= \frac{x}{p} +\frac{w}{0.3} = \frac{x}{p} + \frac{10w}{3}\)
• Now, the distance traveled(in miles) by Emily in the second half of the journey \(= x + w\)

o Speed of Emily(in miles per hour) in the second half of the journey \(= \frac{3}{2}*p\)
o Thus, total time taken(in hours) by Emily to cover the second half of the journey \(= \frac{(x+w)}{\frac{3}{2}p}\)
• So, total time taken(in hours) by complete journey \(= t = \frac{x}{p }+ \frac{10w}{3} + \frac{(x+w)}{\frac{3}{2}p}\)

o Or, \(\frac{5x}{3p} +w(\frac{10}{3} + \frac{2}{3p}) = t\)
\(⟹w \frac{(10p+2)}{3p }= t – \frac{5x}{3p}\)
\(⟹\frac{w(10p+2)}{3p} = \frac{(3pt – 5x)}{3p} \)
\(⟹w= \frac{(3pt – 5x)}{ (10p+2)}\)
\(⟹w= \frac{(1.5pt – 2.5x)}{ (5p+1)}\)