Answer:
The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour
Step-by-step explanation:
<em>Represent the bus average speed with x and the motorcycle average speed with y</em>
Given

Distance covered by bus = 165 miles
Distance covered by motorcycle in same time = 155 miles
Required
Determine the speed of each
Average Speed is calculated as;

Since the two are measured with the same time, represent time with T
For the bus
becomes

Make T the subject of formula

For the motorcycle

Make T the subject of formula

Since, T = T; we have that

Cross Multiply

Substitute 

Open Bracket

Collect Like Terms


Divide both sides by 10

Recall that 


Hence;
<em>The bus travels at 33 miles per hour while the motorcycle travels at 31 miles per hour</em>