Question 476875
You need to add their rates of working
to get their rate working together
For the bigger belt:
Rate1 = (300 pounds of aluminum) / (3 minutes)
For the smaller belt:
Rate2 = (300 pounds of aluminum) / (7 minutes)
I will call moving 300 pounds of aluminum 1 job
So, Rate1 = {{{ 1/3 }}}
and Rate2 = {{{ 1/7 }}}
Let {{{t}}} = time in minutes for both belts to do this job
Rate 1 + rate2 = Rate3
{{{ 1/3 + 1/7 = 1/t }}}
Multiply both sides by {{{21t}}}
{{{ 7t + 3t = 21 }}}
{{{ 10t = 21 }}}
{{{ t = 2.1 }}} min
Note that {{{ .1 }}} min = 6 sec
Working togethers, the belts can move the cans
in 2 min and 6 sec