180/v=t and 180/(v-5)=3+t using t from the first in the second...
180/(v-5)=3+180/v
180/(v-5)=(3v+180)/v cross multiplying...
180v=(3v+180)(v-5)
180v=3v^2-15v+180v-900
3v^2-15v-900=0
v^2-5v-300=0
v^2-20v+15v-300=0
v(v-20)+15(v-20)=0
(v+15)(v-20)=0, since v>0
v=20mph
So the bus usually travels at 20mph
check...
normal...180/20=9 hours
snow...180/15=12 hours
correct.
