A van travels for two hours at an average speed of 40 milles

A van travels for two hours at an average speed of 40 milles per hour. For how long must the van travel at an average speed of 55 miles per hour to raise the overall average speed to 45 miles per hour? What is the total time traveled.

Solution

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