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This Lesson (OVERVIEW of lessons on Travel and Distance) was created by by ikleyn(52756)
  About ikleyn: OVERVIEW of lessons on Travel and DistanceWhat might be better than travels ? - Only Travel and Distance problems. Therefore, there are so many Travel and Distance problems! Below is the list of my lessons on Travel and Distance problems in this site. List of lessons with short annotationsTravel and Distance problemsProblem 1. (Two objects moving toward each other) Two cars entered an Interstate highway at the same time and traveled toward each other. The initial distance between cars was 390 miles. First car was running at the speed of 70 miles per hour, the second car was running at 60 miles per hour. How long will it take for two cars to pass each the other? What distance each car will travel before passing? Problem 2. (Two objects moving in the same direction) Two cars entered an Interstate highway at the same time at different locations and traveled in the same direction. The initial distance between cars was 30 miles. First car was running at the speed 70 miles per hour, the second car was running 60 miles per hour. How long will it take for the first car to catch the second one? What distance each car will travel before the first car catches the second one? Problem 3. (Two objects moving toward each other) Two cars entered an Interstate highway at the same time and traveled toward each other. The initial distance between cars was 390 miles. The speed of the first car was in 10 miles per hour greater than that of the second car. It took 3 hours for two cars to pass each other. What was the speed of each car? What distance each car traveled before they pass each other? Travel and Distance problems for two bodies moving in opposite directions Problem 1. Two motorcycles travel toward each other from cities that are about 950 km apart at rates of 100 km/h and 90 km/h. They started at the same time. In how many hours will they meet? Problem 2. Two cars start from towns 420 miles apart and travel toward each other. They meet at 4 hours. Find the speed of each car if one travels 15 mph faster than the other. Problem 3. Two cyclists, 25 KM apart set out at the same time and meet in 50 minutes. Had they been cycling in the same direction the faster would have overtaken the slower in 5 hours. Find their cycling speeds. Problem 4. Two planes fly in opposite directions. One travels at 475 mi/h and the other at 525 mi/h. How long will it take before they are 7000 miles apart? Problem 5. Two planes start from the same point and fly in opposite directions. The first plane is flying 50 mph slower than the second plane. In 3.5 h, the planes are 2100 miles apart. Find the rate of each plane. Problem 6. Two cars leave Kansas-city, one traveling east and the other west. After 4 hours they are 492 miles apart. If one car is traveling 7 mph faster than the other, find the speed of each car. Travel and Distance problems for two bodies moving in the same direction (catching up) Problem 1. Paul and Sue leave in same direction traveling at 6 km/h and 4 km/h. Paul leaves 1 hour later. When Paul will catch Sue?? Problem 2. A passenger train leaves a train depot 1 hr after a freight train leaves the same depot. The freight train is traveling 15 mph slower than the passenger train. Find the rate of each train if the passenger train over catches the freight train in 3 hrs. Problem 3. A train leaves San Diego at 1:00 pm. A second train leaves the same city in the same direction at 4:00 pm. The second train travels 78 mph faster than the first. If the second train overtakes the first at 6:00 pm, what is the speed of each of the two trains? Problem 4. A bank robber, after completing his heist, jumps into his getaway car and drives away from the scene of a crime, down a straight highway at 40 m/s. A police vehicle follows in pursuit, leaving the bank 2 minutes, after the robber left. If the police travel at 42 m/s, how much time passes from when the bank robber left the bank to when he was caught? Problem 5. A takes 30 minutes to reach a shop from his residence. B takes 20 minutes to reach the same shop from same residence. One day A departed to shop at 8 a.m. If B departed 5 minutes later, at what time B passes A? Problem 6. Two cyclists, 25 KM apart set out at the same time and meet in 50 minutes. Had they been cycling in the same direction the faster would have overtaken the slower in 5 hours. Find their cycling speeds. Using fractions to solve Travel problems Problem 1. The car covers the distance between two cities in 20 hours. The truck can cover this distance in 30 hours. The car and the truck started moving simultaneously from these cities toward each other. When the car and the truck will get passing each other? Problem 2. The car covers the distance between two cities in 4 hours. The truck can cover this distance in 6 hours. The car and the truck started moving simultaneously from these cities in one direction in a way that the car follows the truck. When the car will takeover the truck? Wind and Current problems Problem 1. (Motorboat moving upstream and downstream on a river) A motorboat makes the 24 miles upstream trip on a river against the current in 3 hours. Returning trip with the current takes 2 hours. Find the motorboat speed in still water and the current speed. Problem 2. (Airplane flying into the wind and with the wind) When an airplane flies into the wind, it can travel 3000 miles in 6 hours. When it flies with the wind, it can travel the same distance in 5 hours. Find the speed of the airplane in still air and the speed of the wind. Problem 3. (Motorboat moving upstream and downstream on a river) A motorboat makes an upstream trip on a river in 3 hours against the current, which is of 2 miles per hour. The return downstream trip with the same current takes 2 hours. Find the motorboat speed in still water and the trip length. Problem 4. (Airplane flying into the wind and with the wind) Airplane flies for 6 hours against the wind. The return fly with the same tail wind takes 5 hours. The airplane speed in the still air is 550 miles per hour. Find the wind speed and the fly length. More problems on upstream and downstream round trips Problem 1. On an upstream trip, a canoe travels 40 km in 5 hours. Downstream, it travels the same distance in half the time. What is the rate of the canoe in still water and the rate of the current? Problem 2. A salmon wims 100 m in 8 min downstream. Upstream, it would take the fish 20 min to swim the same distance. What is the rate of the salmon in still water? What is the rate of the current? Wind and Current problems solvable by quadratic equations Problem 1. (Motorboat moving upstream and downstream on a river) A motorboat makes a round trip on a river of 45 miles upstream and 45 miles downstream, maintaining the constant speed 12 miles per hour relative to the water. The entire round trip takes 8 hours. What is the speed of the current? Problem 2. (Airplane flying into the wind and with the wind) An airplane makes a trip of 2400 miles long into the wind and 2400 miles back with the same tail wind, maintaining the constant speed of 440 miles per hour relative to the air. The entire round trip takes 11 hours. Find the speed of the wind. Problem 3. (Motorboat moving upstream and downstream on a river) A motorboat makes a round trip on a river of 45 miles upstream and 45 miles downstream, maintaining the constant speed 12 miles per hour relative to the water. The upstream trip takes two hours more time than the downstream trip. What is the speed of the current? Unpowered raft floating downstream along a river Problem 1. It takes 32 hours for a motorboat moving downriver to get from the pier A to the pier B. The return journey takes 48 hours. How long does it take an unpowered raft to cover the distance from the pier A to the pier B? Problem 2. It takes 5 days for a steamboat to travel from A to B along a river. It takes 7 days to return from B to A. How many days will it take for a raft to drift from A to B? (all speeds stay constant) Selected problems from the archive on the boat floating Upstream and Downstream Problem 1. A canoe traveled Downstream with the current and went a distance of 15 miles in three hours. On the return trip, the canoe traveled Upstream against the current. It took 5 hours to make the return trip. Find the rate of the current. Problem 2. It took an hour for a boat to go six miles upstream. Using the same path, the boat took only 45 minutes to return. What was the speed of the boat in still water? What was the speed of the current? Problem 3. A boat takes 3 hours to go 12 miles upstream. It can go 18 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water. Problem 4. Renee rows a boat downstream for 27 miles. The return trip upstream took 24 hours longer. If the current flows at 4 mph, how fast does Renee row in still water? Selected problems from the archive on a plane flying with and against the wind Problem 1. An airplane flying into a head wind travels the 2400 miles flying distance between two cities in 6 hours. On the return flight, the same distance is traveled in 5 hours. Find the air speed of the plane and the speed of the wind, assuming that both remain constant. (The air speed is the speed of the plane if there were no wind.) Write a system of equations and solve. Problem 2. Making a round trip from Fairview to Cartersville, a distance of 20 miles, a pilot faces 30 mph head wind one way and 30 mph tail wind on the return trip. The return trip takes 45 minutes less than the outbound journey. Find the speed of the plane in still air. Problem 3. A Boeing 747 flies 2420 miles with the wind. In the same amount of time it can travel 2140 miles against the wind. The cruising speed is 507mph. What is the speed of the wind? Selected Travel and Distance problems from the archive Problem 1. A train leaves Orlando at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 12 mph faster than the first. If the second train overtakes the first at 10:00 PM, what is the speed of each of the two trains? Problem 2. It took Andy 9 hours to drive to a rock concert. On the way home, he was able to increase his average speed by 14 mph and make the return drive in only 7 hours. What is his average speed for the drive home? Problem 3. Darren drives to school in rush hour traffic and averages 32 mph. He returns home in mid-afternoon when there is less traffic and averages 48 mph. What is the distance between his home and school if the total traveling time is 1 hr 15 min? Problem 4. Driving from point A to point B at 33 km/h takes 2 hours less than cycling at 11 km/h. How far is it from A to B? Problem 5. A ship made a trip of 231 mi in 14 hours. The ship traveled the first 98 mi at a constant rate before increasing its speed by 5 mph. It traveled another 133 mi at the increased speed. Find the rate of the ship for the first 98 mi. Problem 6. A train travels the distance between the station A and B in 45 minutes. If the train reduces its speed by 5 km per hour it takes 48 minutes to cover this distance, what is the distance between the two stations? Had a car move faster it would arrive sooner Problem 1. A car traveled 1950 miles at a certain speed. Had the car move in 13 mph faster, the trip would be in 5 hours shorter. Find the speed of the car. Problem 2. A biker traveling at his usual speed can go from his house to work in 4 hours. When the weather is bad, he travels 6 miles per hour slower, and it takes him half an hour more. How far is his work from his house? Problem 3. A passenger train's speed is 60 mi/h, and a freight train's speed is 40 mi/h. The passenger train travels the same distance in 1.5 h less time than the freight train. How long does each train take to make a trip? How far do you live from school? Problem 1. How many miles do you live from school if when you drive 45 mph you arrive 1 minute early and when you drive 40 mph you arrive 1 minute late? Problem 2. When a bus travels a certain route at an average speed of 40 km/h it arrives one hour late at its destination, and when it averages 48 km/h it arrives one hour early. What is the length of the journey? How fast should the bus travel in order to arrive on the time at its destination? Problem 3. Sagar and Akash ran 2 km race twice. Akash completed first round two minutes earlier than Sagar. Then in second round Sagar increased speed by 2 km/hr; then Sagar finished the round 2 minutes earlier than Akash. Find their speed of running in the first round. One unusual Travel problem Problem 1. Jonny on his bicycle and Kevin on his motorcycle started to move simultaneously at 8:00 am from the points A and B on a road toward each other. Each is moving at his own constant speed. Jonny and Kevin met at noon (12 o'clock at midday) and continued to move without stopping each on his way at the same speed. Kevin arrived to the point A at 2:00 pm. At what time Jonny arrived to the point B? Another unusual Travel problem (Arnold's problem on two walking old women) Problem 1. Two old women started at sunrise and each walked at a constant velocity. One went from A to B and the other from B to A on the same road. They met at noon and, continuing with no stop, arrived respectively at B at 4 p.m. and at A at 9 p.m. At what time was the sunrise that day? Problem 2. Winnie and Piglet decided to visit one another and set off at the same time to each others house. When they met on the road joining their houses, they forgot that they wanted to see each other and continued walking. Winnie reached Piglet's house 8 minutes after the meeting and Piglet got to Winnie's house 18 minutes after the meeting. How long did it take Piglet to reach Pooh's house from the time he left his own house? Calculating an average speed: a train going from A to B and back Problem 1. A train goes from New Orleans to Boston at 40 mph (miles per hour). On the way back it returns at a speed of 80 mph. Certainly, it takes less time to return. What is the average speed of the train? Problem 2. A train goes from A to B at a speed of u. On the way back it returns at a speed of v. Certainly, it takes different time to return. What is the average speed of the train on the way from A to B and back? One more problem on calculating an average speed Problem 1. A train averaged 120 Find its average speed for the last 20% of the trip. Travel problem on a messenger moving back and forth along the marching army's column Problem 1. An army of troops is marching along a road at 5 mph. A messenger on horseback was sent from the front to the rear of the column and returns immediately back. The total time taken being 10 minutes. Assuming that the messenger rides at the rate of 10 mph, determine the length of the column. Problem 2. A battalion 20 miles long advances 20 miles. During this time, a messenger on a horse travels from the rear of the battalion to the front and immediately turns around, ending up precisely at the rear of the battalion upon the completion of the 20-mile journey. How far has the messenger traveled? A person walking along the street and buses traveling in the same and opposite directions Problem 1. As Kyle walked along a street at a constant speed, he noticed that every 12 minutes, a bus passed him traveling in the same direction, and every 4 minutes, a bus passed him traveling in the opposite direction as Kyle was walking. If all of the buses travel at a constant speed and leave the terminals at each end of the street at equally spaced intervals, how many minutes long is that interval? Clock problems Problem 1. What is the angle between the large (minute) hang and the small (hour) hang at 11:55 pm? Problem 2. What is the angle between the large (minute) hang and the small (hour) hang at 12:05 am? Problem 3. As you know, at noon the minute hang and the hour hang of a clock coincide. When the minute hang and the hour hang coincide (have the same direction) for the first time after the noon? Problem 4. As you know, at 6:00 pm the minute hang and the hour hang of a clock lie in one straight line and have the opposite directions. When the minute hang and the hour hang will lie in one straight line and have the opposite directions for the first time after 6:00 pm? Problem 5. When the minute hang of a clock will be perpendicular to the hour hang for the first time after 2:00 pm? When such an event will happen for the next time? Problem 6. Current time is about 1:07 pm, and the large hang and the small hang on a clock have (almost) the same direction. When such an event will happen for the next time? In other words, when the large (minute) hang and the small (hour) hang will have the same direction the next time? Advanced clock problems Problem 1. It was 9:00 am and the algebra quiz was about to begin. The students were told that they could only work on the quiz until the hands of the clock pointed in the same direction. How long did they have to work? Problem 2. It is now between 9 am and 10 o'clock am. In 4 minutes, the hour hand of a clock will be directly opposite the position occupied by the minute hand 3 minutes ago. What time is it? Problem 3. It is now past 3 o'clock in the afternoon. The minute hand 3 minutes from now will be directly opposite the hour hand 9 minutes ago. What time is it? Problem 4. The time is past 2 o'clock. In 10 minutes, the minute hand will be as much ahead of the hour hand as it is now behind it. What time is it? Problem 5. It is between 2 and 3 pm. A person looking his watch mistakes the hour hand for the minute hand and thinks that the time of the day is 55 minutes earlier than it really is. What is the true time? Problems on bodies moving on a circle Problem 1. Jenna and Nina are running laps around the outside of their house. They both start at the front door at the same time. Jenna takes 18 seconds to run all the way around. Nina takes 20 seconds. If they maintain the same speed, how long will it be before they are both at the front door at the same time again? Problem 2. Two cars, A and B, are driving in the same direction on a circular track, making one loop after the other. Car A takes 5 minutes to drive one whole loop. Car B makes the same in 7 minutes. The cars started simultaneously from the point P on the road. When the cars A and B will be simultaneously at the point P next time? Problem 3. Tracy and Kelly are running laps on the indoor track at steady speeds, but in opposite directions. They meet every 20 seconds. It takes Tracy 45 seconds to complete each lap. How many seconds does it take for each of Kelly's laps? Problem 4. Two track-men are running on a circular race track 300 feet in circumference. Running in opposite directions, they meet every 10 seconds. Running in the same direction, the faster passes the slower every 50 seconds. Find their rates in feet per second. A train passing a telegraph post and passing a bridge Problem 1. A train takes 4 seconds to pass a telegraph post and 20 seconds to pass a 256 m long bridge. Find the length of the train and its speed. A train passing a platform Problem 1. A train which has a length of 90 meters is traveling at a speed of 36 kilometers per hour. It passes a platform 120 meters long. How long does it take the train to pass the platform from the moment the front of the train comes up to the closest end of the platform to the moment the rear of the train comes up to the other end of the platform? Problem 2. A train 120 meters long is running with a speed of 54 kilometers per hour. The train passes a platform in 20 seconds. It is the time from the moment the front of the train comes up to the closest end of the platform to the moment the rear of the train comes up to the other end of the platform. What is the length of the platform (in meters)? Problem 3. A train of d units long is traveling at a speed v units per second. It passes a platform of L units long. How long does it take the train to pass the platform from the moment the front of the train comes up to the closest end of the platform to the moment the rear of the train comes up to the other end of the platform? Solve the problem analytically (get the general formula). Problem 4. A train which has a length of It enters a tunnel 1 mile long. How long does it take the train to pass through the tunnel from the moment the front enters to the moment the rear leaves the tunnel? A train passing through a tunnel Problem 1. A train which has a length of How long does it take the train to pass through the tunnel from the moment the front enters the tunnel to the moment the rear leaves it? Problem 2. A train 300 meters long is running with a speed of 45 Problem 3. A train which has a length of d units, is traveling at a speed v units per second. It enters a tunnel of L units long. How long does it take the train to pass through the tunnel from the moment the front enters the tunnel to the moment the rear leaves it? Solve the problem analytically (get the general formula). Problem 4. A train which has a length of 90 meters, is traveling at a speed of 36 kilometers per hour. It passes a platform 120 meters long. How long does it take the train to pass the platform from the moment the front of the train comes up to the closest end of the platform to the moment the rear of the train comes up to the other end of the platform? A light-rail train passing a walking person Problem 1. A light-rail train was running at a constant speed on a straight railway, and a person was walking in the same direction on a sidewalk parallel to the railway. The pedestrian noticed that it took 4 second from the moment when the front of the first light-trail cart came up to him to the moment when the rear of the last light-rail cart came up. Find the speed of the light-rail train if its length was 20 meters and the speed of the walking person was 3.6 kilometers per hour. Problem 2. A light-rail train was running at a constant speed on a straight railway, and a person was walking in the same direction on a sidewalk parallel to the railway. The pedestrian noticed that it took t second from the moment when the front of the first light-trail cart came up to him to the moment when the rear of the last light-rail cart came up. Find the speed of the light-rail train if its length was L meters and the speed of the walking person was w kilometers per hour. Solve the problem analytically (get the general formula). A train passing another train Problem 1. Two trains move on parallel tracks in opposite directions. The first train has the length of 200 m and moves at a speed of 72 kilometers per hour. The second train has the length of 150 m and moves at a speed of 54 kilometers per hour. How long will it take for two trains to pass each the other? The passing time is counted starting from the moment when the front of the first train's locomotive comes up to the front of the second train's locomotive to the moment when the rear of last cart of the first train comes up to the rear of the last car of the second train. Problem 2. Two trains move on parallel tracks in the same direction. The first train has the length of 200 m and moves at a speed of 72 kilometers per hour. The second train has the length of 150 m and moves at a speed of 54 kilometers per hour. The first train follows the second one and catching it. How long will it take for the first train to pass the second one? The passing time is counted starting from the moment when the front of the first train's locomotive comes up to the rear of the last cart of the second train's to the moment when the rear of last cart of the first train comes up to the front of the locomotive of the second train. A man crossing a bridge and a train coming from behind Problem 1. A man is three eighths of the way across a bridge when he hears a train coming from behind. If he runs as fast as possible back toward the train, he will get off the bridge just in time to avoid a collision. Also, if he runs as fast as possible away from the train, he will get off the bridge (on the other side) just in time to avoid a collision. The train is traveling at 60 miles per hour. How fast does the man run? A rower going on a river who missed the bottle of whiskey under a bridge Problem 1. A rower goes upstream on a river. When passing under a bridge, a bottle of whiskey falls into the water. Since it's half-full, it floats. The rower doesn't notice it, and continues going upstream. After 20 minutes, he gets thirsty and looks for the bottle. Having sobered some, he figures out that it fell into the water. He turns around and rows downstream. He finds the bottle 1 mile from the bridge. Find the speed of the current. Non-traditional Travel and Distance problems Problem 1. A truck traveling at 40 kph and a car traveling at 50 kph leave town A at the same time and travel to a second town B. Upon reaching B, the car turn around immediately and traveled the same road toward A. Find the distance between the towns if the car will meet the truck 30 km from town B. Problem 2. Ryan and Nelson are in the middle of running a lap around a track. The circumference of the track is 400 feet. Ryan is 60 feet behind Nelson. Nelson is running at 6 ft/s. How fast should Ryan run so that they both complete the lap in 30 seconds? Problem 3. When a van is driven without stopping its speed is 54 km/h and when it is driven with stops place to place then its speed is 45 km/h. For how long the van is stopped per hour? Problem 4. Three friends Anil, Bala and Chetan, traveled from town X to town Y which was 40 km apart. Anil who had a bike started along with Bala while Chetan started simultaneously on foot. After some time, Anil dropped Bala on the way and went back to pick up Chetan while Bala proceeded to Y on foot. Anil picked up Chetan and reached Y at the same time as Bala. Anil traveled at 50km/hr. The speed at which Bala and Chetan walked was 10 km/hr. Find the time after which Anil turned back? Problem 5. Ramesh and Narendra start from the same place and arrive at another place in 40 minutes and 60 minutes respectively. If Narendra starts 10 minute earlier than Ramesh, how much time Ramesh will take to reach Narendra. The distance covered by a free falling body during last second of the fall Problem 1. A body falls freely from the top of the tower and during last second of the fall, it falls through 25 m. Find the height of tower. The Doppler Shift Problem 1. While driving a car, Al honks the horn every 5 seconds. Bill is standing by the side of the road and hears the honks of the oncoming car every 4.6 seconds. The speed of sound is 330 meters per second. Calculate the speed of Al's car. Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I. This lesson has been accessed 9160 times. |
