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A car and a truck leave towns \(230 \mathrm{mi}\) apart, traveling toward each other. The car travels 15 mph faster than the truck. They pass each other 2 hr later. What are their rates?

In his motorboat, Bill travels upstream at top speed to his favorite fishing spot, a distance of \(36 \mathrm{mi}\), in 2 hr. Returning, he finds that the trip downstream, still at top speed, takes only \(1.5 \mathrm{hr}\). Find the rate of Bill's boat and the rate of the current. Let \(x=\) the rate of the boat and \(y=\) the rate of the current.

Solve each system using the substitution method. If a system is inconsistent or has dependent equations, say so. $$ \begin{array}{l} x=5 y \\ 5 x-25 y=5 \end{array} $$

The perimeter of a triangle is \(70 \mathrm{~cm}\). The longest side is \(4 \mathrm{~cm}\) less than the sum of the other two sides. Twice the shortest side is \(9 \mathrm{~cm}\) less than the longest side. Find the length of each side of the triangle.

Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. $$ \begin{aligned} 7 x+2 y &=6 \\ -14 x-4 y &=-12 \end{aligned} $$

Three kinds of tickets are available for a rock concert: "up close," "in the middle," and "far out." "Up close" tickets cost \(\$ 10\) more than "in the middle" tickets. "In the middle" tickets cost \(\$ 10\) more than "far out" tickets. Twice the cost of an "up close" ticket is \(\$ 20\) more than three times the cost of a "far out" ticket. Find the price of each kind of ticket.

Solve each system using the elimination method. If a system is inconsistent or has dependent equations, say so. $$ \begin{array}{l} 3 x+3 y=0 \\ 4 x+2 y=3 \end{array} $$

The National Hockey League uses a point system to determine team standings. A team is awarded 2 points for \(a\) win \((\mathrm{W}), 0\) points for a loss in regulation play \((\mathrm{L}),\) and 1 point for \(a n\) overtime loss (OTL). Use this information to solve each problem. $$ \begin{array}{|l|c|c|c|c|c|} \hline{\text { Team }} & \text { GP } & \text { W } & \text { L } & \text { OTL } & \text { Points } \\ \hline\text { Anaheim } & 82 & & & & 105 \\ \hline\text { Edmonton } & 82 & 47 & 26 & 9 & 103 \\ \hline\text { San Jose } & 82 & 46 & 29 & 7 & 99 \\ \hline\text { Calgary } & 82 & 45 & 33 & 4 & 94 \\ \hline\text { Los Angeles } & 82 & & & & 86 \\ \hline \end{array} $$ During the \(2016-2017\) NHL regular season, the Anaheim Ducks played 82 games. Their wins and overtime losses resulted in a total of 105 points. They had 10 more losses in regulation play than overtimes losses. How many wins, losses, and overtime losses did they have that season?

The National Hockey League uses a point system to determine team standings. A team is awarded 2 points for \(a\) win \((\mathrm{W}), 0\) points for a loss in regulation play \((\mathrm{L}),\) and 1 point for \(a n\) overtime loss (OTL). Use this information to solve each problem. $$ \begin{array}{|l|c|c|c|c|c|} \hline{\text { Team }} & \text { GP } & \text { W } & \text { L } & \text { OTL } & \text { Points } \\ \hline\text { Anaheim } & 82 & & & & 105 \\ \hline\text { Edmonton } & 82 & 47 & 26 & 9 & 103 \\ \hline\text { San Jose } & 82 & 46 & 29 & 7 & 99 \\ \hline\text { Calgary } & 82 & 45 & 33 & 4 & 94 \\ \hline\text { Los Angeles } & 82 & & & & 86 \\ \hline \end{array} $$ During the same NHL regular season, the Los Angeles Kings also played 82 games. Their wins and overtimes losses resulted in a total of 86 points. They had 4 more total losses (in regulation play and overtime) than wins. How many wins, losses, and overtime losses did they have that season?