A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing tou
ches on a house they built. Working alone, Irina can paint a certain room in 9 hours. Paulo can paint the same room in 8 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth
Since Irina can paint 1 room in 9 hours, that means she paints 1/9 of the room in 1 hour. Her portion of the equation would be 1/9x, with x being the number of hours she works and 1/9 of a room per hour being her speed. Since Paulo can paint 1 room in 8 hours, that means he paints 1/8 of the room in 1 hour. His portion of the equation would be 1/8x, with x being the number of hours he works and 1/8 of a room per hour being his speed. The equation would then be 1/9x + 1/8x = 1 (Irina's portion of the room, plus Paulo's portion of the room, equal to one whole room). Find a common denominator. 72 is the first number that both 9 and 8 divide evenly into. Since 9*8 = 72, we multiply the top of 1/9 by 8 to convert the fraction and get 8/72x. Since 8*9 = 72, we multiply the top of 1/8 by 9 to convert the fractio and get 9/72x. We now have 8/72x+9/72x=1 17/72x=1 Divide both sides by 17/72: 17/72x ÷ 17/72 = 1÷17/72 x=1/1 ÷ 17/72 x=1/1 * 72/17 x=72/17=4.24 Together it should take them 4.24 hours.
