Solving Rate Problems: Assignment

In training for a triathlon, Yuna swam 1.9 miles in the open ocean, which took her 2 hours. For the first part of her swim, she averaged 1.4 miles per hour. For the second part of her swim, she swam against the current and started to tire, so her average speed decreased to 0.8 mph. What was the distance of the first part of Yuna's swim? Round to the nearest tenth as needed. The distance in the first part of her swim was _____ miles.

0.7

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?

B. 3r+3/8=1

It takes 12 minutes to fill an entire bathtub using both the cold and hot water. If just the cold water is used, it takes 18 minutes to fill the bathtub. How long would it take to fill the bathtub if just the hot water were used? The equation __________________ can be used to solve for the rate, r, for the hot water alone to fill the bathtub. The hot water can fill _________ of the tub in 1 minute. It would take _____ minutes for the hot water to fill the bathtub.

Blank One: (12/18)+12r=1 Blank Two: 1/36 Blank Three: 36

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?

D. 600t = 480(18 - t)

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.

2. Armand and Jill will travel the same amount of time to meet 3. The equation used to find the time, t, it will take for them to meet is 50t + 60t = 247.5. 5. Jill will travel 135 miles to meet Armand.

Talia took the bus from her home to the bank and then walked back to her home along the same route. The bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. To determine the time, x, that it took Talia to walk home, she used the equation40(0.9 - x) = 5x. The time of Trip 2 is ___ hours. The distance of Trip 1 is ___ km.

Blank One: 0.8 Blank Two: 4

Eitan is on a train heading west into the city while Dmitri is on a train on the adjacent track heading east, away from the city. They start 150 miles apart. Eitan's train is traveling at an average speed of 65 miles per hour while the average speed of Dmitri's train is 55 miles per hour. How long will it take the two trains to reach each other? How far outside the city will they be? The time when the two trains reach each other is ____ hours. The trains are ____ miles away from the city when they reach each other.

Blank One: 1.25 hours Blank Two: 68.75 miles

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 ____ km/h. The time of Trip 1 is _____ hours.

Blank One: 5 Blank Two: 0.9-x

Alejandro rode his bike to work at an average rate of 15 miles per hour. To go home, he put his bike on the front rack of the bus and took the bus home along the same route, traveling at an average rate of 22.5 miles per hour. If Alejandro's bike ride to work took 45 minutes, how many hours did the bus ride home take?

C. 0.5 hours

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.

C. 3.4 hours

Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes. If Roni and Allie work together to mow the field, what part of the field would Roni mow?

C. about 0.71 of the field