Preparing for Standardized Tests
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Start by finding the unit rate of puzzles per hour that can be completed by Hana and Eric, individually.
D
We are told that Hana can finish a puzzle in 6 hours and Eric can do it in 5 hours. We will find the time t that it would take for them to do the job together. Let's start by finding the unit rate of puzzles per hour
that can be completed by Hana and Eric, individually.
Hana's Rate: & 1 puzzle/6hours [0.75em]
Eric's Rate: & 1 puzzle/5 hours
Note that the product of rate and time gives the fraction of the job done. We can multiply each rate by the time t to represent the amount of the job done by each person.
| People | Rate (puzzle/hour) | Fraction of the Job Done |
|---|---|---|
| Hana | 1/6 | 1/6 t |
| Eric | 1/5 | 1/5 t |
The sum of the fractions that represent the amount of the job done by each person will be equal to 1. 1/6 t+1/5 t= 1 We will solve this equation by multiplying both sides of the equation by the least common denominator (LCD).
It would take them about 2.7 hours to finish the puzzle together, which corresponds to option D.