Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
-Three trains  one eastbound, one westbound, and one northbound  leave a city at the same time. The speed of the northbound train is 10 miles per hour greater than the speed of the eastbound train. After 2 hours, the
Distance between the westbound train and the eastbound train is 200 miles. Twice the speed of the westbound
Train is 100 miles per hour more than the speed of the northbound train. Find the speeds of the three trains.
A) eastbound, 40 mph; westbound, 70 mph; northbound, 30 mph
B) eastbound, 20 mph; westbound, 80 mph; northbound, 40 mph
C) eastbound, 30 mph; westbound, 70 mph; northbound, 40 mph
D) eastbound, 40 mph; westbound, 70 mph; northbound, 50 mph

Question

Quizplus · Accepted Answer

To solve this, we set up equations based on the information given. Let $E$ be the speed of the eastbound train, $W$ be the speed of the westbound train, and $N$ be the speed of the northbound train. We know that $N = E + 10$. The distance between the westbound and eastbound trains after 2 hours is 200 miles, so $2E + 2W = 200$. Finally, twice the speed of the westbound train is 100 mph more than the speed of the northbound train, so $2W = N + 100$. Substituting $N = E + 10$ into the last equation and solving the system of equations gives us $E = 30$ mph, $W = 70$ mph, and $N = 40$ mph.

Given the Cost Function, C(x), and the Revenue Function, R(x)