A forest fire is burning in a valley. Officials estimate that if the fire burns for h hours, the cost of the lost timber is 1000h dollars. They estimate that x firefighters can stop the fire in 3600/x hours. The cost for each firefighter is $20 (for transportation) plus $25 per hour (for salary, meals, and other overhead). A. Let C be the cost of the fire (including the cost of the firefighters and the lost timber). C will depend on both h (how many hours the fire burns) and x (the number of firefighters sent to fight it) Give a formula for C in terms of x and h. B. Give a formula that relates x and h C. How many firefighters should be used if the cost C of the fire is to be minimized? Justify your solution.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
4. A forest fire is burning in a valley. Officials estimate that if the fire burns for h hours, the cost of the lost timber is 1000h dollars. They estimate that x firefighters can stop the fire in 3600/x hours. The cost for each firefighter is $20 (for transportation) plus $25 per hour (for salary, meals, and other overhead).
A. Let C be the cost of the fire (including the cost of the firefighters and the lost timber). C will depend on both h (how many hours the fire burns) and x (the number of firefighters sent to fight it) Give a formula for C in terms of x and h.
B. Give a formula that relates x and h
C. How many firefighters should be used if the cost C of the fire is to be minimized? Justify your solution.
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