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) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the bus in km/hr
+s+%2B+40+ = the speed of the police car in km/hr
Let +t = time in hrs for both
----------------
For police car:
(1) +5+=+%28+s+%2B+40+%29%2At+
For bus:
(2) +3+=+s%2At+
----------------------
(2) +t+=+3%2Fs+
and
(1) +5+=+%28+s+%2B+40+%29%2A%283%2Fs%29+
(1) +5s+=+3%2A%28+s+%2B+40+%29+
(1) +5s+=+3s+%2B+120+
(1) +2s+=+120+
(1) +s+=+60+
+s+%2B+40+=+100+
The speed of the bus is 60 km/hr
The speed of the police car is 100 km/hr
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check:
(1) +5+=+%28+s+%2B+40+%29%2At+
(1) +5+=+%28+60+%2B+40+%29%2At+
(1) +5+=+100t+
(1) +t+=+.05+ hr
and
(2) +3+=+s%2At+
(2) +3+=+60t+
(2) +t+=+.05+ hr
OK

Answer by ikleyn(52864) About Me  (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

P%2FB = 5%2F3.        (2)


From (2), express P = %285%2F3%29%2AB and substitute it into equation (1). You will get

%285%2F3%29%2AB+-+B = 40.


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

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


Then B = 120%2F2 = 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.