25] Two places A and B are 160 km apart on a highway. One car starts from A and another car B
at the same time. If they travel in the same direction they meet in 8 hours. But if they travel
towards each other they meet in 2 hours. Find the speed of both the cars A and B.
Answers
Answer:
i hope this will help you
Answer:
A = 50 km/h
B = 30 km/h
Step-by-step explanation:
In second case, both the cars A and B move towards each other, so let their meeting point be Q.
_____________________
A------------>Q<-----------------B
Given that the total distance between them is 160 km, therefore,
AQ + BQ = 160 ......(1)
we know that distance(d) = speed(s) × time(t), let the speed of the cars A and B be x and y respectively, then,
AQ = 2x
BQ = 2y
2x + 2y = 160 .......by eqn(1)
x + y = 160/2
x + y = 80 .......(2)
In the first case, both the cars move in the same direction, let us consider their meeting point as Q again.
____________________________
A -----------------------------------------------> Q
B-------------->Q
Let us take the speeds of both the cars same as we took earlier, then,
AQ - BQ = 160 ......(3)
AQ = 8x
BQ = 8y
8x - 8y = 160 .......by the eqn(3)
x - y = 160/8
x - y = 20 .......(4)
if we will solve the eqns (2) and (4), we will get,
x = 50 km/h
y = 30 km/h
Therefore, the speeds of both the cars A and B are 50 km/h and 30 km/h respectively.