The airspeed of a plane is its speed in the absence of wind. With a headwind, ground speed (the actual speed in relation to the ground) is decreased by the speed of the wind. With a tailwind, ground speed is increased by the speed of the wind. Let A denote the airspeed of a plane and W the speed of the wind, both in miles per hour. Suppose it takes the plane 9 hours to travel the 720 miles from one town to another facing a headwind of W. The return trip, now with a tailwind of W, takes only 3 hours. (a) Express the ground speed on the trip out in terms of A and W. (b) Use the information from part (a) and the fact that distance equals rate times time to find an equation involving A and W for the trip out. (c) Express the ground speed on the return trip in terms of A and W
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
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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.
The airspeed of a plane is its speed in the absence of wind. With a headwind, ground speed (the actual speed in relation to the ground) is decreased by the speed of the wind. With a tailwind, ground speed is increased by the speed of the wind. Let A denote the airspeed of a plane and W the speed of the wind, both in miles per hour. Suppose it takes the plane 9 hours to travel the 720 miles from one town to another facing a headwind of W. The return trip, now with a tailwind of W, takes only 3 hours.
(b) Use the information from part (a) and the fact that distance equals rate times time to find an equation involving A and W for the trip out.
(d) Use the information from part (c) and the fact that distance equals rate times time to find an equation involving A and W for the return trip.
| A = | ______ |
| W = | ______ |
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