Chapter 6.5, Problem 14PPS

To determine

To find the length of each tour

Answer to Problem 14PPS

Crystal Palace Tour: 2.17 miles

Horseshoe Lake Tour: 1.33 miles

Explanation of Solution

Given:

Length of both the tours: 3.5 miles

Crystal palace tour is half a mile less than twice the length of the Horseshoe Lake Tour.

Calculation:

Let x be the length of the Crystal Palace Tour and y be the length of the Horseshoe Lake Tour.

Given that the length of both the tours is 3.5 miles.

  $\Rightarrow x+y=\mathrm{3.5.....................}(1)$

Also, Crystal palace tour is half a mile less than twice the length of the Horseshoe Lake Tour.

  $\Rightarrow x=2y-\mathrm{0.5................}(2)$

Substitute equation (2) in equation (1),

  $\begin{array}{l}\Rightarrow (2y-0.5)+y=3.5\\ \Rightarrow 3y=4\\ \Rightarrow y=1.33\end{array}$

Substitute the value of y in equation (2),

  $\begin{array}{l}\Rightarrow x=2(\frac{4}{3})-0.5\\ \Rightarrow x=\frac{8}{3}-0.5\\ \Rightarrow x=\frac{8-1.5}{3}\\ \Rightarrow x=2.17\end{array}$

Conclusion:

Therefore, the length of the Crystal Palace Tour is 2.17 miles and the length of the Horseshoe Lake Tour is 1.33 miles.