Question

Two cars a and b start simultaneously from a certain place at the speed of 30 km/h and 45 km/h, respectively. The car b reaches the destination 2 h earlier than a. What is the distance between the starting point and destination

Answer 1

Since, the car B reaches the destination 2 h earlier than A

so, let the time taken by car A = t
and the time taken by car B = t - 2

let the distance be = D ( the distance is same for both the cars )

Distance of car A = speed of car A × time taken by car A

=> D = 30 × t

=> D = 30t -----------> ( 1 )

Distance of car B = speed of car B × time taken by car B

=> D = 45 × ( t - 2 )

=> D = 45( t - 2 )

=> D = 45t - 90 -----------> ( 2 )

Substituting (1) and (2) we get:

=> 30t = 45t - 90

=> 30t - 45t = -90

=> -15t = -90

=> t = $\frac{-90}{-15}$

=> t = $\frac{90}{15}$

=> t = 6

Since, we have calculated the speed and time of the cars..we can find out the distance travelled

Average Distance = (Speed of car A × time taken by car A)
=> D = 30 × t

=> D = 30 × 6

=> D = 180 km

--------- OR ---------

Average Distance = (Speed of car B × time taken by car B)
=> D = 45 × ( t - 2 )

=> D = 45 × (6 - 2)

=> D = 180 km