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?

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.