Question 183627
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r
Average Rate (or speed)=(Total Distance)/(Total Time)

Let t=amount of time the van must travel at 55 mph
And let d=distance travelled

Total Distance travelled=(80+d)
Total Time travelled=(2+t)
Average Speed=45 mph
So:
45=(80+d)/(2+t)-----------------------eq1
and
d=55t------------------------------------eq2
substitute d=55t from eq2 into eq1:
45=(80+55t)/(2+t)  multiply each side by (2+t)
45(2+t)=80+55t or
90+45t=80+55t subtract 80 and also 45t from each side
90-80+45t-45t=80-80+55t-45t  collect like terms
10=10t
t= 1 hr-----------------amount of time van must travel at 55 mph

CK
45=(80+55)/3
45=135/3
45=45


Hope this helps---ptaylor