SOLUTION: a police car is moving 40 kph faster than a bus. the time that it takes the bus to travel 3 km, police car can travels 5 km. find their speeds

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Question 1086557: a police car is moving 40 kph faster than a bus. the time that it takes the bus to travel 3 km, police car can travels 5 km. find their speeds
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the speed of the bus in km/hr
= the speed of the police car in km/hr
Let = time in hrs for both
----------------
For police car:
(1)
For bus:
(2)
----------------------
(2)
and
(1)
(1)
(1)
(1)
(1)

The speed of the bus is 60 km/hr
The speed of the police car is 100 km/hr
----------------------------------------
check:
(1)
(1)
(1)
(1) hr
and
(2)
(2)
(2) hr
OK

Answer by ikleyn(52866)   (Show Source): You can put this solution on YOUR website!
.
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

 = .        (2)


From (2), express P =  and substitute it into equation (1). You will get

 = 40.


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

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


Then B =  = 60.

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


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

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

Solved.


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