Question

A snowstorm causes a bus driver to decrease the usual average rate a 180 mile route by 5 miles per hour. As a result , the bus takes three hours longer than usual to complete the route. At what average rate does the bus usually cover a 180 mile route?

Answer 1

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.