Question 533119
Let {{{ p }}} =  the penguin's speed in feet/min
Let {{{ d }}} = distance covered by Batman until he catches Penguin
Batman's speed = {{{ 3p }}}
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given:
Penguin's head start was {{{ 3*1200 = 3600 }}} ft
Start a stopwatch when Batman leaves. Now they both run
for the same amount of time
Batman:
(1) {{{ d = 3p*30 }}}
Penguin:
(2) {{{ d - 3600 = p*30 }}}
Substitute (1) into (2)
(2) {{{ 90p - 3600 = 30p }}}
(2) {{{ 60p = 3600 }}}
(2) {{{ p = 60 }}}
and
{{{  3p = 180 }}}
Penguin ran 60 ft/min
Batman ran 180 ft/min
check:
(1) {{{ d = 3p*30 }}}
(1) {{{ d = 3*60*30 }}}
(1) {{{ d = 5400 }}}
and
(2) {{{ d - 3600 = p*30 }}}
(2) {{{ 5400 - 3600 = p*30 }}}
(2) {{{ 1800 = 30p }}}
(2) {{{ p = 60 }}}
OK