Question

A minibus takes 6 hours less to cover 1680 km distance, if its speed is increased by 14 km/h? what is the usual time taken by minibus?

Answer 1

Let speed of Minibus is x km/h 
time taken by Minibus is T hour 

  ∵ speed = distance/time 
x = 1680/T ⇒ T = 1680/x --------------------(1) 


now, A/C to question,
 if Minibus increased his speed by 14 km/h, then time taken by him is 6 hour less to cover 1680 km distance.
   e.g.,time taken with xkm/h - time taken by (x + 14) km/h = 6 hours
⇒ 1680/x - 1680/(x + 14) = 6 
⇒ 1680[14/(x² + 14x)] = 6 
⇒ 280 × 14 = x² + 14x 
⇒ x² + 70x - 56x - 3920 = 0
⇒ x = -70 , 56 
hence, speed of Minibus is 56 km/h 
put x = 56 in equation (1) ,
 T = 1680/56 = 30 hours 
   

Answer 2

Let X be the speed .

According to question , speed of bus after increasing the speed=(X+14)kmph -----------(1)
Let us consider A as Source and B as destination:
A_______________ 1680Km_______________B

In Case I:
Time taken to cover the distance 1680Km:
Time= distance/Speed
=1680/x------------(equation i)

In Case II:
Time taken to cover distance of 1680km=1680/x+14

Time difference=6 hrs

[1680/x]-1680/(x+14)=6

[1680[x+14] -1680x]/x[x+14]=6

1680x14=6[x[x+14]23520 =6

x²+84x6x²+84x-23520=0

by taking 6 common

x²+14x-3920=0

x²+70x-56x-3920=0

x(x+70)-56(x+70)=0

x=-70 , 56

speed cannot be zero:

So X=56km/h
Substitute the value in equation 1 we get
T=1680/56=30 Hours