two pipes running simultaneously can fill a tank in 2 hours and 40minutes.after the lager pipe had run for 3hours the smaller pipe was also turned on the tank was full 40minutes later how long would it take each pipe a;one to fill the tank
问题描述:
two pipes running simultaneously can fill a tank in 2 hours and 40minutes.after the lager pipe had run for 3hours the smaller pipe was also turned on the tank was full 40minutes later
how long would it take each pipe a;one to fill the tank
答
4;8
答
两个管子同时同时开放2小时40分可排空水箱,大管子开放3小时后,小管子也打开,40分钟后水箱排空,每个管子单独开放多长时间排空?
2小时40分-40分=2小时,
大管子3小时的工作量相当于两个管子2小时的工作量,即大管子的效率占总效率的2/3,小管子占1/3
大管子所用时间是两管子同时开的3/2倍,小管子所用时间是两管子同时开的3倍(效率与时间成反比)
2小时40分*3/2=4小时
2小时40分*3=8小时
方程:
设大管子效率为x,两管总效率为1/(8/3)=3/8
3x+(2/3)(3/8)=1
x=1/4
3/8-1/4=1/8
1/(1/4)=4小时(大)
1/(1/8)=8小时(小)