Concept explainers
APPLICATIONS
Halfway Point Two friends live in the city described in Exercise 53, one at the corner of 3rd St. and 7th Ave. and the other at the corner of 27th St. and 17th Ave. They frequently meet at a coffee shop halfway between their homes.
(a) At what intersection is the coffee shop located?
(b) How far must each of them walk to get to the coffee shop?
53. Distances in a City A city has streets that run north and south and avenues that run east and west, all equally spaced. Streets and avenues are numbered sequentially, as shown in the figure. The walking distance between points A and B is 7 blocks—that is, 3 blocks east and 4 blocks north. To find the straight-line distance d, we must use the Distance Formula.
(a) Find the straight-line distance (in blocks) between A and B.
(b) Find the walking distance and the straight-line distance between the corner of 4th St. and 2nd Ave and the corner of 11th St and 26th Ave.
(c) What must be true about the point P and Q if the walking distance between P and Q equals the straight-line distance between P and Q?
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Chapter 1 Solutions
Algebra and Trigonometry (MindTap Course List)
- Halfway Point Two friends live in the city described in Exercise 53, one at the corner of 3rd St. and 7th Ave. and the other at the comer of 27th St. and 17th Ave. They frequently meet at a coffee shop halfway between their homes. At what intersection is the coffee shop located? How far must each of them i1k to get to the coffee shop?arrow_forwardAPPLICATIONS Distance, Speed, and Time John and Mary leave their house at the same time and drive in opposite directions. John drives at 60 mi/h and travels 35 mi farther than Mary, who drives at 40 mi/h. Marys trip takes 15 min longer than Johns. For what length of time does each of them drive?arrow_forwardAirplane Speed Two planes start from Los Angeles International Airport and fly in opposite directions. The second plane starts 12 hour after the first plane, but its speed is 80 kilometers per hour faster. Two hours after the first plane departs, the planes are 3200 kilometers apart. Find the airspeed of each plane.arrow_forward
- Airplane Speed Two planes start from Los Angeles International Airport and fly in opposite directions. The second plane starts 12 hour after the first plane, but its speed is 80 kilometers per hour faster. Find the speed of each plane when 2 hours after the first plane departs the planes are 3200 kilometers apart.arrow_forwardDistance and Time Anthony leaves Kingstown at 2:00 P.M. and drives to Queensville, 160 mi distant, at 45 mi/h. at 2:15 P.M. Helen leaves Queensville and drives to Kingstown at 40 mi/h. At what time do they pass each other on the road?arrow_forwardShadow Length A person who is 6 feet tall walks away from a 50-foot tower toward the tip of the tower’s shadow. At a distance of 32 feet from the tower, the person’s shadow begins to emerge beyond the tower’s shadow. How much farther must the person walk to be completely out of the tower’s shadow?arrow_forward
- Flying Speed Two planes leave simultaneously from Chicago’s O ’Hare Airport, one flying due north and the other due east (see figure). The northbound plane is flying 50 miles per hour faster than the eastbound plane. After 3 hours, the planes are 2440 miles apart. Find the speed of each plane.arrow_forwardDistances n a City A city has street that run north and south and avenues that run east and west, all equally spaced. Streets and avenues are numbered sequentially, as shown in the figure. The walking distance between points A and B is 7 blocks— that is, 3 blocks east and 4 blocks north. To find the straight line distance d, we must use the Distance Formula. Find the straight-line distance (in blocks) between A and B. Find the walking distance and the straight-line distance between the corner of 4th St. and 2nd Ave. and the corner of 11th St. and 26th Ave. What must he true about the points P and Q if the walking distance between P and Q equals the straight-line distance between P and Q?arrow_forwardSurveying A surveyor in a helicopter is determining the width of an island, as shown in the figure. (a) What is the shortest distance d the helicopter must travel to land on the island? (b) What is the horizontal distance x the helicopter must travel before it is directly over the nearer end of the island? (c) Find the width w of the island. Explain how you found your answer.arrow_forward
- Speed of a Boat Two fishing depart a harbour at the same time, one traveling east, the other south. The eastbound boat travels at a speed 3mi/h faster than the southbound boat. After two hours the boats are 30 mi apart. Find the speed of the southbound boat.arrow_forwardWidth of a Lawn A factory is to be built on a lot measuring 180 ft by 240 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of this lawn be, and what are the dimensions of the factory?arrow_forwardIsocost Equation We are to buy quantities of two items: n1 units of item 1 and n2 units of item 2. a. If item 1 costs 3.50 per unit and item 2 costs 2.80 per unit, find a formula that gives the total cost C, in dollars, of the purchase. b. An isocost equation shows the relationship between the number of units of each of two items to be purchased when the total purchase price is predetermined. If the total purchase price is predetermined to be C=162.40 dollars, find the isocost equation for items 1 and 2 from part a. c. Solve for n1 in the isocost equation you found in part b. d. Using the equation from part c, determine how many units of item 1 are to be purchased if 18 units of item 2 are purchased.arrow_forward
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