On a family trip, 100 miles were traveled at a rate of 60 miles per hour and another 30 miles at 40 miles per hour , what is the average speed for this trip

Average speed = total distance / total time (i)

here total distance = 100+30 = 130 miles

time = distance / speed

time for step 1 = t1 = 100/60 = 1.6667 hours
time for step 2 = t2 = 30/40 = 0.75 hours

so total time = t = t1+t2 =2.416667hours

put values of distance and time in equation (i) we get

average speed = 130 / 2.416667 = 53.79 = 53.8 miles per hour