let

v1 = 60 mi/h the average rate to the destination

v2 = 40 mi/h the average rate back

t = the time of the trip to there

t + 1 = the time of the trip back (return trip takes 1 h longer than the trip there)

a. Let d be the distance in miles the family traveled to visit their relatives. How many hours did it take to drive there.

since the distance = average speed*time we have:

v1*t = v2*(t + 1)

60t = 40(t + 1)

by solving we find

t = 2 hr

click here to see the step by step solution of the equation:

it took 2 hours to drive there.

b. in terms of d how many hours did it take to make the return trip

d = 40(t + 1)

40(t + 1) = d

by solving for t we find

t = (d - 40)/40

click here to see the step by step solution of the equation:

c. Writ and solve an equation to determine the distance the family drove to see their relatives. What was the average rate for the entire trip.

d = v1*t

d = 60*2

d = 120 mi

the distance the family drove to see their relatives is 120 miles.

the average rate of the entire trip (back and forth) v is equal to the total distance traveled divided by the total time of the trip:

v = (2d)/(t + t + 1)

v = (2*120)/(2 + 2 + 1)

v = 240/5

v = 48 mph

the average rate for the entire trip was 48 mph.