Question 1086557
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<pre>
Let P be the speed of police car (in km/h), and
let B be the speed of the bus.


First condition says

P - B = 40.     (1)


The second condition says

{{{P/B}}} = {{{5/3}}}.        (2)


From (2), express P = {{{(5/3)*B}}} and substitute it into equation (1). You will get

{{{(5/3)*B - B}}} = 40.


Multiply both sides by 3 to rid of denominator. You will get

5B - 3B = 120,   or  2B = 120.


Then B = {{{120/2}}} = 60.

Thus we found that the bus' speed is 60 km/h.


Then the police car speed is  60 + 40 = 100 km/h.
</pre>

<U>Answer</U>.  60 km/h for the bus and 100 km/h for police car. 


Solved.