题目
Linda takes 4 hours to do a job, whereas Bob takes 6 hours to do the same job. They worked together at their respective rates but Bob took two breaks of equal duration during the time. Despite that, the two of them were able to complete the job in 2 hours 30 minutes. What is the duration of each break that Bob took. ?
解析
琳达1小时能完成\(\frac{1}{4}\)份工作,鲍勃1小时能完成\(\frac{1}{6}\)份工作。两人合作,1小时能完成\(\frac{1}{4}+\frac{1}{6}=\frac{5}{12}\)份工作。
现在,他们1小时能完成\(\frac{5}{12}\)份工作
在2.5小时内,他们能完成\(\frac{5}{12} \times \frac{5}{2} = \frac{25}{24}\)份工作
从题目可知,他们实际在2.5小时内完成了整份工作。因此,因为鲍勃中途休息,他们少完成了\(\frac{25}{24}-1=\frac{1}{24}\)份工作。
鲍勃1小时能完成\(\frac{1}{6}\)份工作
鲍勃完成\(\frac{1}{24}\)份工作需要\(\frac{6}{24}=\frac{1}{4}\)小时,也就是15分钟。
这15分钟等于鲍勃休息的2次总时长。因此,每次休息的时长为\(\frac{15 \times 60}{2}=450\)秒。