Question

Question 108

Solve the following

Distance between two plates A and B is 210 km. Two cars start simultaneously from A and B in opposite directions and distance between them after 3 hours is 54 km. If speed of one car is less than that of other by 8 km/h, then find the speed of each.

Answer 1

Let the speed of car starts from A be x km/h.
Then, speed of car starts from B=(x+8) km/h
Given, distance between the cars after 3h=54km
According to the question,
Total distance between A and B - Total distance covered by both cars in 3h=54
$\Rightarrow 210-[3x+3(x+8\left)\right]=54$ $[\because =speed\times time]$
$\Rightarrow 210-3x-3x-24=54\Rightarrow -6x=-210+24+54\Rightarrow -6x=-210+78\Rightarrow -6x=-132\Rightarrow x=-132\times \left(\frac{-1}{6}\right)\therefore x=22$
Hence, the speed of car starts from A =22 km/h
and the speed of car starts from b=22+8=30 km/h