A car is driving along a highway at 55kph. The driver notices a bus, 1/2 km behind.The bus passes the car one minute later.What was the speed of the bus?

Question

I am actually a math challenger..and yeah...i'm not that quite smart..so thats why i badly need help in answering this question.

Answer 1

The Earth is rotating on it's axis.  The Earth is revolving around our Sun.  Our solar system is moving ...  so the "highway" in this problem should not be considered a fixed reference point (although you may compute the relative speeds using it).
 
The restatement of the problem (after you re-read and understand it) could be, "What is 1/2 km per minute in kph?  Add that to 55 kph."  {note: any restatement of a problem should eliminate TMI (too much information) and make it more of a math problem that is easy to solve.)
 
To change units without changing the value, we use the Multiplicative Identity (that is, 1).
        (1/2 km) per minute
        ( (1/2 km) / (1 minute) ) * 1
        ( (1/2 km) / (1 minute) ) * ( (60 minutes)/(1 hour) )
        (1/2)(60) km/hr                        [minutes cancel]
          30 kph
 
  55 kph + 30 kph = 85 kph
 
Let's verify:
 

  In one minute,

      the bus travels (D=RT):    (85 kph)*(1 min) * ( 1 hr)/(60 min) ) = 1416 2/3 meters

      the car has driven:           (55 kph)*(1 min) * ( 1 hr)/(60 min) )  =  916 3/3 meters

Difference:                                                                        1/2 km =  500      meters

Answer 2

Think of the bus and car as 1/2 km apart.  If both the bus and car are going 55 kph, the gap never closes.  But the bus closes that 1/2 km in one minute or 1/60 of an hour.  Speed is distance divided by time, so to close the 1/2 km gap in 1/60 hour, the bus was going (1/2)/(1/60) = 60/2 = 30 kph faster than the car = 55 kph + 30 kph = 85 kph.