Question 476024
How many miles head start does the 1st bus have?
{{{ d[1] = 42*2 }}}
{{{ d[1] = 84 }}} mi
Start a stopwatch when the 2nd bus enters interstate.
Both will now travel for the same amount of time
until bus 2 catches bus 1. Call this time {{{t}}}.
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Let {{{d}}} = distance bus 2 has to go to catch bus 1
For bus 2:
(2) {{{ d = 66t }}}
For bus 1:
(1) {{{ d- 84 = 42t }}}
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Substitute {{{d}}} in (2) for {{{d}}} in (1)
(1) {{{ 66t - 84 = 42t }}}
(1) {{{ 24t = 84 }}}
(1) {{{ t = 3.5 }}}
It takes the 2nd bus 3.5 hrs to catch 1st bus
check:
(2) {{{ d = 66t }}}
(2) {{{ d = 66*3.5 }}}
(2) {{{ d = 231 }}}
and
(1) {{{ d - 84 = 42t }}}
(1) {{{ 231 - 84 = 42*3.5 }}}
(1) {{{ 147 = 147 }}}
OK