OAR Math Skills: Word Problems Flashcards

A submarine travels at a constant speed of 20 knots for 3 hours and then increases its speed by 25% for the next 2 hours. How many nautical miles has the submarine traveled in total?

Answer: 110 nautical miles

First, calculate the distance traveled in the first 3 hours: 20 knots * 3 hours = 60 nautical miles. Next, calculate the new speed: 20 knots * 1.25 = 25 knots. Then, calculate the distance traveled in the next 2 hours: 25 knots * 2 hours = 50 nautical miles. Finally, add the two distances together: 60 + 50 = 110 nautical miles.

A supply shipment contains rations, water, and medical kits in a ratio of 5:4:1. If there are a total of 500 items in the shipment, how many of the items are water?

Answer: 200

The ratio 5:4:1 represents a total of 5 + 4 + 1 = 10 parts. To find the value of one part, divide the total number of items by the total number of parts: 500 / 10 = 50 items per part. Since water represents 4 parts of the ratio, multiply the value of one part by 4: 50 * 4 = 200.

A rectangular deck has a perimeter of 60 feet. If the length of the deck is 6 feet longer than its width, what is the area of the deck in square feet?

Answer: 208 sq ft

The formula for the perimeter of a rectangle is P = 2(l + w). We are given P = 60 and l = w + 6. Substitute these into the formula: 60 = 2((w + 6) + w), which simplifies to 60 = 2(2w + 6), then 60 = 4w + 12. Solving for w gives 48 = 4w, so w = 12 feet. The length is l = 12 + 6 = 18 feet. The area is A = l * w, so A = 18 * 12 = 216 square feet. Oh, wait, let me re-calculate: 18 * 12 = 216. My final answer calculation was incorrect. Let's re-calculate A = 18 * 12. 10*18=180, 2*18=36. 180+36 = 216. Rechecking the algebra: 60 = 2(l+w), 30 = l+w. l = w+6. 30 = (w+6) + w. 30 = 2w + 6. 24 = 2w. w=12. l = 12+6=18. Area = 12 * 18 = 216 sq ft. Let me check my options. 216 is an option. I made a mistake in my initial selection. Let me re-check the calculation one more time. Perimeter = 2(18+12) = 2(30)=60. Correct. Length is 6 feet longer than width (18 is 6 more than 12). Correct. Area is 18*12=216. Correct. The correct answer is 216 sq ft.

A piece of equipment originally priced at $1,200 is on sale for 20% off. An officer can receive an additional 10% discount on the sale price. How much will the officer pay for the equipment, excluding tax?

Answer: $864

First, calculate the sale price after the initial 20% discount: $1,200 * 0.20 = $240. The sale price is $1,200 - $240 = $960. Next, calculate the additional 10% discount on the sale price: $960 * 0.10 = $96. The final price is the sale price minus the additional discount: $960 - $96 = $864.

A team can assemble 3 widgets every 45 minutes. How many full widgets can the team assemble during an 8-hour shift?

Answer: 32

First, determine the rate of assembly per hour. If 3 widgets are made in 45 minutes (0.75 hours), the rate is 3 widgets / 0.75 hours = 4 widgets per hour. Then, multiply this rate by the number of hours in the shift: 4 widgets/hour * 8 hours = 32 widgets.

Two planes depart from the same airport at the same time, traveling in opposite directions. Plane A travels at 450 mph and Plane B travels at 525 mph. How many hours will it take for them to be 3,900 miles apart?

Answer: 4 hours

Since the planes are traveling in opposite directions, their speeds are combined to find the rate at which the distance between them is increasing. Combined speed = 450 mph + 525 mph = 975 mph. To find the time it takes to be 3,900 miles apart, divide the distance by the combined speed: Time = Distance / Speed = 3900 miles / 975 mph = 4 hours.