Answer
a) $2$ hours
b) $d=40t+40$
c) $120$ miles; $48\text{ mi/hr}$
Work Step by Step
Using $d=rt$, with $r_{\text{visit}}=60$, then
$$
d_{\text{visit}}=60t
.$$
With $r_\text{return}=40$,
$$
d_{\text{return}}=40(t+1)
.$$
a) Since the distances of the trip visit and the return trip are the same, then
$$\begin{aligned}
d_\text{visit}&=d_\text{return}
\\
60t&=40(t+1)
\\
60t&=40t+40
\\
20t&=40
\\
t&=2
.\end{aligned}$$Hence, the travel time, $t$, to visit is $2$ hours.
b) The return trip, $d_\text{return}$, is given by
$$\begin{aligned}
d_\text{return}&=40(t+1)
\\&=
40t+40
.\end{aligned}$$Hence, in terms of $d$, the return trip is given by $d=40t+40$.
c) Using $d_\text{visit}=60t$, with $t=2$, then
$$
d_\text{visit}=60(2)=120
.$$Hence, the distance the family drove to visit their relatives is $120$ miles.
The total distance of the entire trip is $2(120)=240\text{ mi}$. The total time of the entire trip is $t+(t+1)=2+3=5\text{ hours}$. Hence, the average rate of the entire trip is
$$\begin{aligned}
d&=rt
\\
240&=r(5)
\\
r&=48
.\end{aligned}$$Hence, the average rate, $r$, of the entire trip is $48\text{ mi/hr}$.
