Benedict left his house to go to the library. He took the first bus, which travelled 5 km in $t$ minutes. He then alighted at a bus stop and waited for 12 minutes to switch to the next bus. The second bus took 2 minutes less than the first bus to reach his destination after travelling a further 3.75 km.

1. Express and add all parts of the journey time

First bus time $=t$ minutes.

Waiting time $=12$ minutes.

Second bus time $=t-2$ minutes.

Total time
$=t+12+(t-2)=2t+10$

1. Find the total distance and express the total time in hours

Total distance travelled
$=5+3.75=8.75\text{ km}.$
From part (a), total time $=2t+10$ minutes.

In hours, total time
$=\frac{2t+10}{60}\text{ h}.$

2. Form an equation using average speed

Using
$\text{average speed}=\frac{\text{total distance}}{\text{total time}},$
$10.5=\frac{8.75}{\frac{2t+10}{60}}.$

3. Solve the equation and find the total time

$10.5=\frac{8.75\times 60}{2t+10}$
$10.5(2t+10)=525$
$2t+10=50$
Hence the total time taken is
$50\text{ minutes}.$