All practice questions

A medical evacuation helicopter is dispatched from its base camp to pick up a patient at a rural hospital $120$ miles away. The pilot flies to the hospital at a steady speed of $120$ mph. Due to heavy headwinds on the way back, the helicopter's average speed for the entire round trip drops to $80$ mph. What is the helicopter's average speed, in mph, during the return flight?

A logistics supply convoy has a strict operational window of $72$ hours to complete its route. The first leg of the journey takes $1$ day, $9$ hours, and $45$ minutes. The second leg takes $830$ minutes. Before the final leg, the crew takes a mandatory rest period of $4.5$ hours. How many minutes remain in the $72$-hour operational window for the convoy to complete the final leg?

A Coast Guard search-and-rescue aircraft executes a mission over the ocean. It first flies directly to the designated search zone at an average speed of $180\text{ mph}$ for $1$ hour and $20$ minutes. Once inside the zone, it slows to a search speed of $120\text{ mph}$, flying a grid pattern for $2$ hours and $15$ minutes. After completing the grid, it returns to base along a direct route at $150\text{ mph}$ for $48$ minutes. What is the total distance flown by the aircraft during the entire mission, in miles?

A topographic map uses a scale of $\frac{3}{8}\text{ inch} = 15\text{ miles}$. A rectangular section of a national forest is shown on this map with dimensions of $1\frac{1}{2}\text{ inches}$ by $2\frac{1}{4}\text{ inches}$. If a conservation program plans to plant $400$ trees per square mile throughout this entire section, how many thousands of trees will be planted in total?

A military cargo aircraft flies from Base Alpha to Base Bravo at an average speed of $300$ miles per hour. Upon arrival, the aircraft spends exactly $1$ hour and $30$ minutes on the ground being loaded. It then returns to Base Alpha along the exact same route at an average speed of $600$ miles per hour. If the total elapsed time for the entire mission, from the initial departure to the final return, was $7$ hours and $30$ minutes, what was the aircraft's overall average speed, in miles per hour, for the entire mission?

A homeowner is applying a protective sealant to a rectangular wooden patio that completely surrounds a rectangular swimming pool. The overall dimensions of the patio and pool together are $40\text{ feet}$ long and $30\text{ feet}$ wide. The swimming pool inside measures $25\text{ feet}$ long and $15\text{ feet}$ wide. One gallon of sealant covers exactly $150\text{ square feet}$ of wood and costs $\$28$. If the homeowner must purchase whole gallons of sealant, what is the total cost, in dollars, of the sealant required for the wooden patio?

An interior designer is planning to cover a rectangular accent wall with custom wallpaper. The wall measures $15\text{ feet}$ in width and $8\text{ feet}$ in height. If the wallpaper costs $\$4$ per square foot, what is the total cost, in dollars, of the wallpaper needed for this wall?

A rectangular reservoir for a water purification system measures $20$ feet long, $15$ feet wide, and $10$ feet deep. Safety protocols dictate that the reservoir must never exceed $90\%$ of its total volume capacity. The reservoir currently contains $900$ cubic feet of water. If a high-capacity pump adds water to the reservoir at a rate of $60$ cubic feet per minute, how many minutes will it take for the water to reach the maximum allowed capacity?

A carpenter is preparing to install baseboards in a room. One specific section of the wall requires a continuous board that is exactly $2$ yards and $2$ feet long. What is the required length of this board in inches?

A cylindrical well is being drilled into the ground. The well has a diameter of $36\text{ inches}$ and a target depth of $70\text{ feet}$. If soil is extracted from the well at a constant rate of $11\text{ cubic feet per hour}$, how many hours will it take to drill the well completely? (Use $\frac{22}{7}$ for $\pi$)

A circular water pipe has a diameter of $8$ inches. What is the cross-sectional area of the pipe? Use $\pi = 3.14$.

A contractor is applying a specialized primer to a rectangular warehouse wall that is $60\text{ feet}$ long and $18\text{ feet}$ high. The wall contains a rectangular loading bay door measuring $30\text{ feet}$ long and $12\text{ feet}$ high, which will not receive the primer. If the primer material costs $\$15$ per square yard, what is the total cost, in dollars, of the primer needed for the wall?

A coffee shop prepares cold brew coffee in large batches. Each batch produces exactly $3$ gallons and $2$ quarts of cold brew. The shop needs to completely fill three $4$-gallon dispensers and two $2$-gallon dispensers. If the shop has already prepared $704$ fluid ounces of cold brew, how many additional full batches must they prepare today to have enough cold brew to exactly fill all the dispensers?

A landscaper is designing a circular flower bed with a diameter of $10$ feet. She needs to install a flexible plastic border completely around the outer edge of the flower bed. What is the total length, in feet, of the plastic border needed? Use $\pi = 3.14$.

A university is installing artificial turf on an indoor practice facility. The rectangular facility measures $120\text{ feet}$ in length and $60\text{ feet}$ in width. Inside the facility, there are two identical rectangular equipment zones, each measuring $30\text{ feet}$ long and $15\text{ feet}$ wide, which will remain bare concrete and will not be covered with turf. If the artificial turf costs $\$24$ per square yard, what is the total cost, in dollars, of the artificial turf needed for the facility?

A military convoy must travel a total distance of $540$ miles to reach a forward operating base. To ensure they arrive on schedule, they need to maintain an overall average speed of $45$ miles per hour for the entire journey.

During the first segment, they travel $150$ miles in exactly $150$ minutes. During the second segment, they travel $135$ miles at an average speed of $30$ miles per hour.

What average speed, in miles per hour, must the convoy maintain for the remainder of the trip to meet their target overall average speed?

A community center is building a new rectangular sandbox for the playground. The sandbox measures $6$ feet long, $4$ feet wide, and $1.5$ feet deep. How many cubic feet of sand are required to fill the sandbox completely to the top?

A warehouse worker is stacking identical shipping boxes. Each box is exactly $16$ inches tall. If the worker creates a single stack of $3$ boxes, what is the total height of the stack in feet?

A supply sergeant is reviewing the specifications for a rectangular storage pod. The pod has a known total volume of $120$ cubic feet. If the pod measures $6$ feet in length and $4$ feet in width, what is the height of the pod in feet?

A military transport vehicle has circular tires with a diameter of $4$ feet. If the vehicle moves forward such that each tire makes exactly $250$ full revolutions without slipping, what is the total distance traveled in feet? Use $\pi = 3.14$.