Question 1080135
The rate for the large conveyor belt is:
{{{ 300/9 = 100/3 }}} pounds/min
The rate for the smaller belt is:
{{{ 300/45 = 20/3 }}}
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Let {{{ t }}} = time in minutes for the 2 belts
used together to move {{{ 300 }}} pounds
Add their rates to get rate working together
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{{{ 100/3 + 20/3 = 300/t }}}
Multiply both sides by {{{ 3t }}}
{{{ 100t + 20t = 900 }}}
{{{ 120t = 900 }}}
{{{ t = 7.5 }}}
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Both belts used together take 7 min 30 sec to
move 300 pounds of cans
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check:
{{{ 100/3 + 20/3 = 300/t }}}
{{{ 100/3 + 20/3 = 300/7.5 }}}
{{{ 33.333 + 6.667 = 40 }}}
{{{ 40 = 40 }}}
OK