Solving rate problems

Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading east at an average speed of 220 kilometers per hour. At the same time, Lian boards a train heading west on a parallel track at an average speed of 250 kilometers per hour. How far has Lian traveled when the two trains pass each other?

1,000 kilometers

Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours.Which equation can be used to find the time it took Stu to hike the trail?

3t = 5(3 - t), trip to the end of trail- 3;t;3t, trip back- 5;3-t;5(3-t).

Working together, Alex and Millie can file all the papers in the file cabinets in 4 hours. It would have taken Alex 6 hours to do the job alone. What is the missing value in the table that represents the part of the papers that Alex would file if Alex and Millie worked together?

4/6

It would take Marco 6 hours to paint a fence by himself. It would take Jaylyn 5 hours to paint the same fence by herself. Marco is creating this table to help him determine how long it would take them to paint the fence together. Which heading should be written above the first column of numbers?

Rate (part/hour)

Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours. The equation 3t = 5(3 - t) can be used to find the time it took Stu to hike one way. How long did it take Stu to hike the trail one way? How long is the trail? What is the total distance Stu travelled?

A.1.875; B.5.625; C.11.25

It takes 5 minutes to fill the sink using only the cold water. If both the hot water and the cold water are turned on, it takes 2 minutes to fill the sink. Which is the correct table that can be used to determine x, the time in minutes it takes to fill the sink using only the hot water?

c

Armand and Jill are 247.5 miles apart, and driving toward each other. Armand is driving at a rate of 50 miles per hour and Jill is driving at a rate of 60 miles per hour.Use the scenario and table to determine which statements are true. Check all that apply.

1.Armand and Jill will travel the same amount of time to meet, 2. The equation used to find the time, t, it will take for them to meet is 50t + 60t = 247.5, 3. Jill will travel 135 miles to meet Armand.

Jonas jogged up the hill at an average rate of of a mile per minute and then walked down the hill at an average rate of of a mile per minute. The round trip took him 42 minutes. What is the missing value in the table that represents the distance of the trip down the hill?

1/16(42 - x)

Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?

18 minutes

Working together, Sam and Charlie can change all the light bulbs in the office building in 3 hours. It would have taken Charlie 8 hours to do the job alone.Which equation can be used to solve for the rate, r, for Sam to change all the light bulbs in the office building by himself?

3r + 3/8= 1

The average rate of the first part of Yi's walk on a park loop was 4 miles per hour. She then met up with a friend and the two walked the rest of the way at an average rate of 5 miles per hour. The entire 3-mile walk took Yi 42 minutes (0.7 hour). Which equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend?

4x + 5(0.7 - x) = 3

Milla and Luka are 3 kilometers apart and walking toward each other. Milla's average speed is 5 kilometers per hour and Luka's is 4 kilometers per hour. Which equation can be used to find t, the time it takes for Milla and Luka to meet?

5t + 4t = 3

An airplane flew at an average rate of 600 miles per hour from Tokyo to Seattle. Because of a strong headwind, the average rate of the return trip was only 480 mph. The round trip took 18 hours.Which equation can be used to determine the time for each leg?

600t = 480(18 - t)

Talia took the bus from her home to the bank and then walked back to her home along the same route. The round trip took 0.9 hours total. The bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. Use the table to complete these statements.The rate of Trip 2 is?The time of Trip 1 is?The time of Trip 2 is?The distance of Trip 1 is?

A.5 km/h, B.0.9-x hours, trip 1- 40; 0.9-x; 40(0.9-x), trip 2- 5;x;5x, 0.8 hours, 4km.

A medium water hose can fill a pool in 30 minutes. A larger water hose can fill the same pool in 20 minutes. If both hoses are turned on at the same time, how long will it take to fill the pool?What equation can be used to solve this work problem?How many minutes will it take both hoses to fill the pool?

A.t/3+t/2=1,B. 12 min, medium horse- 1/30;t;1/30t, large horse- 1/20;t;1/20t.

Sanjay and Felipe are putting together a 500-piece puzzle. Sanjay could do the entire puzzle by himself in 6 hours, while it would take Felipe 8 hours to do the puzzle alone.Use the table to write and solve an equation to determine the approximate amount of time it would take Sanjay and Felipe to do the puzzle if they were working together.

3.4 hours

Amanda and Alexis live 4 miles apart. They decide to start walking toward each other's houses at the same time. Amanda walks at a rate of 3.5 miles per hour and Alexis walks at a rate of 4 miles per hour. How long will it take for them to meet? Round to the nearest hundredth of an hour. [Remember: D = (r)(t)]

0.53 hour

Irina rode her bike to work at an average speed of 16 miles per hour. It started to rain, so she got a ride home along the same route in her coworker's car at an average speed of 27 miles per hour. If Irina's ride home in the car took 24 minutes (0.4 of an hour), how many hours was her bike ride to work, to the nearest tenth of an hour?

0.7 of an hour

If Jasper installs a floor himself, it will take him 7 hours. Working with Yolanda, it will take them 3 hours.If they work together, what is the missing value in the table that represents the part of the floor Jasper will install?

1/7(3)