Solving Rate Problems Answers

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 equation 40(0.9 – x) = 5x. The time of Trip 2 is hours. The distance of Trip 1 is km.

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?

Which equation can be used to determine the time for each leg?

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.

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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.

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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?

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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 . The trains are away from the city when they reach each other.

Which equation represents the relationship between r and t?

The rate of Trip 2 is km/h.

The time of Trip 1 is hours.