Question 111994
Let {{{d[1]}}}=distance bus #1 travels and {{{d[2]}}}=distance bus #2 travels


So we want to know when their distance apart is 274 miles. So this means


{{{d[1]+d[2]=274}}}



Now using the distance-rate-time equation, we get


{{{d[1]=44t}}} Here r=44 mph


Since the 2nd bus starts 1 hour later, it's traveling time is 1 hour less. So t is really {{{t-1}}}


{{{d[2]=48(t-1)}}} Here r=48 mph



{{{d[2]=48t-48}}} Distribute






{{{d[1]+d[2]=274}}} Now go back to the first equation


{{{44t+48t-48=274}}} Plug in {{{d[1]=44t}}} and {{{d[2]=48t-48}}}





{{{92t-48=274}}} Combine like terms on the left side



{{{92t=274+48}}}Add 48 to both sides



{{{92t=322}}} Combine like terms on the right side



{{{t=(322)/(92)}}} Divide both sides by 92 to isolate t




{{{t=7/2}}} Reduce


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Answer:

So our answer is {{{t=7/2}}}  (which is approximately {{{t=3.5}}} in decimal form)



So the first bus was on the road for 3.5 hours (which if added to 1:00 pm gets you 4:30 pm)


So at 4:30 pm the two buses are 274 miles apart