Question

Two towns A and B are 365km apart. A bus left town A at 8;15a.m and travelled towards town B at 60km/hr. At 9.00a.m a car left town B towards town A at a speed of 100km/hr. The two vehicles met at town c which lies between town A and B.

1. Find the time of the day the two vehicles met.
2. Find the distance between towns A and C.
3. At town C the driver of the car took 1 hour for lunch and followed the bus back to town B. Find how fast must the car move to arrive at town B same time as the bus. 

Answer 1

1. Relative speed=60+100=160Km/hr
   Relative distance= 365 − (⁴⁵/₆₀ × 60)
                           =320km
      320  =   2hrs
      160     +9       
                   11.00a.m
   ALT
   
   ⁴⁵/₆₀ × 60 = 45km
   ∴  x  =  320−x
      60      100
   100x =19200−60
   160x =19200
        x=120km
   120  =2hrs
    60
   9+2=11.00am
    
2. 45 + 120=165km
3. Bus=60 × 1 =60km
   Bus to cover 140km
   Car to cover 200km
   200  = 140
     x        60
   x=200 × 60
            140
   x=85.71km/h