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- RHEA CAN PAINT A ROOM IN 4 HOURS. DESTINY CAN PAINT THE SAME ROOM IN 6 HOURS. HOW LONG WOULD IT TAKE FOR BOTH RHEA AND DESTINY TO PAINT THE ROOM IF THEY ARE WORKING TOGETHER? A COMMON MISTAKE FOR THIS TYPE OF PROBLEM IS TO ADD THE AMOUNT OF TIME IT TAKES RHEA TO PAINT THE ROOM ALONE TO THE TIME IT TAKES DESTINY TO PAINT THE ROOM ALONE, WHICH WOULD BE A TOTAL OF 10 HOURS AND THEN DIVIDE BY 2 GIVING A WRONG ANSWER OF 5 HOURS. IT DOESNT MAKE SENSE IT WOULD TAKE 5 HOURS IF THEYRE WORKING TOGETHER WHEN RHEA CAN PAINT THE ROOM ALONE IN 4 HOURS, WHICH IS LESS TIMES. SO TO START THIS TYPE OF PROBLEM WE WANT TO FIRST LIST THE RATE AT WHICH RHEA AND DESTINY CAN PAINT THE ROOM PER HOUR. SO RHEAS RATE, SINCE SHE CAN PAINT THE ROOM IN 4 HOURS WILL BE 1/4 OF THE ROOM PER HOUR AND BECAUSE DESTINY CAN PAINT THE ROOM IN 6 HOURS, HER RATE IS 1/6 OF THE ROOM PER HOUR. SO IF WE LET T EQUAL THE NUMBER OF HOURS, NOTICE IF THEY PAINT FOR 1 HOUR, RHEA WOULD PAINT 1/4 OF THE ROOM WHILE DESTINY WOULD PAIN
