Time, Rate, and Distance

A courier drives from a dispatch center to a client's location $60$ miles away and then returns to the dispatch center along the exact same route. The outbound drive to the client takes exactly $2$ hours. If the courier's average speed for the entire round trip is $24$ miles per hour, what is the courier's average speed on the return trip?

A rescue helicopter flies at a rate of $3$ miles per minute for $40$ minutes to reach an extraction point. After the pickup, it flies to a hospital at a cruising speed of $120$ miles per hour for $90$ minutes. What is the total distance the helicopter traveled in miles?

A ferry transports vehicles from the mainland to an island $18$ miles away. The ferry travels to the island at a speed of $9$ miles per hour and returns to the mainland along the same route at a speed of $6$ miles per hour.

How many hours does the complete round trip take?

A cyclist travels from her home to a nearby town, a distance of $15$ miles, at an average speed of $12$ mph. On the return trip along the same route, her average speed is $20$ mph. What is her average speed, in mph, for the entire round trip?

A logistics convoy leaves a supply depot and travels at a steady speed of 40 miles per hour for 2 hours and 15 minutes. After a 45-minute halt to refuel, the convoy resumes its route at a speed that is 20% faster than its initial speed. It travels at this new speed for 1 hour and 40 minutes until reaching the forward operating base. What is the total distance traveled by the convoy, in miles?

A pilot flies a cargo plane from Airport A to Airport B at an average speed of $240$ mph. The pilot returns along the exact same route, but due to a strong headwind, the return flight averages only $160$ mph. If the total flying time for the entire round trip was exactly $5$ hours, what is the one-way distance between Airport A and Airport B, in miles?

A cyclist rides from his home to a nearby park $12$ miles away at a speed of $12$ miles per hour. He returns home along the same route at a speed of $6$ miles per hour. What is his average speed for the entire round trip in miles per hour?

A military cargo plane flies for $2$ hours and $20$ minutes at an average speed of $420$ miles per hour. It then encounters a strong headwind, reducing its average speed to $360$ miles per hour for the remaining $45$ minutes of the flight. What is the total distance, in miles, traveled by the cargo plane?

A cargo aircraft flies from a logistics hub to a regional airport, a one-way distance of $360$ miles. The aircraft makes the outbound journey at an average speed of $180$ mph. On the return trip along the exact same route, carrying a heavier load, it travels at an average speed of $120$ mph. What is the aircraft's average speed for the entire round trip?

A high-speed passenger train travels between two major cities. It covers the first segment of the journey at an average speed of $120\text{ mph}$ for $1\text{ hour and } 45\text{ minutes}$. Due to track maintenance, it reduces its speed to $40\text{ mph}$ for $36\text{ minutes}$. After clearing the maintenance zone, it accelerates and travels at $150\text{ mph}$ for $48\text{ minutes}$ to reach its final destination. What is the total distance of the trip?

A military convoy must complete a 180-mile route to a forward operating base in exactly 4 hours. The convoy travels at an average speed of 50 mph for 90 minutes, then halts for a 60-minute security checkpoint. What average speed, in mph, must the convoy maintain for the remainder of the journey to arrive exactly on time?

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 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 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 mountain rescue snowmobile is dispatched to retrieve a stranded hiker. It travels from base camp to the hiker's location at an average speed of $30$ miles per hour. Carrying the extra passenger on the return trip, the snowmobile heads back along the exact same trail at an average speed of $20$ miles per hour. If the total driving time for the entire rescue mission is $90$ minutes, what is the total round-trip distance traveled by the snowmobile?

A rescue helicopter departs base at $0915$ hours for a distress signal $120$ miles away. It flies outbound at $160$ mph, spends $30$ minutes on scene, and returns along the same route at $120$ mph. At what time does the helicopter arrive back at the base?

A military convoy is traveling along a straight highway at a constant speed of $45\text{ miles per hour}$. A scout vehicle leaves the rear of the convoy and travels forward to reach the front of the convoy. The total length of the convoy is $1.5\text{ miles}$, and the scout vehicle travels at a constant speed of $88\text{ feet per second}$. How many minutes does it take for the scout vehicle to reach the front of the convoy? ($1\text{ mile} = 5,280\text{ feet}$)

A supply train needs to deliver equipment to a base that is 110 miles away. For the first 1 hour and 20 minutes, the train travels at a steady rate of 30 mph. Due to track repairs, the train must travel at exactly 20 mph for the remainder of the trip. What is the total travel time from the start of the journey until the train arrives at the base?

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 reconnaissance patrol must complete a $24$-mile route with an overall average speed of $4$ mph to meet their extraction window. For the first $10$ miles, difficult terrain limits their average speed to $5$ mph. After completing this section, the patrol halts for exactly $120$ minutes to observe an objective. To achieve the required overall average speed, what must be their average speed, in mph, for the remaining distance?