Question

Two persons 27km apart, starting at the same time meet each other in 9 hours, if they walk in the same direction and 3 hours if they walk in opposite directions. Find their speed of walking.

Answer 1

Hint: Now we know that distance = speed × time. Let the speed of A and B be x and y. Hence we can calculate the distance travelled by A and B. Now in the first scenario A travels 27km more than B. Hence we have that distance travelled by A + 27 = distance travelled by B. Similarly in the second scenario we have the sum of distance travelled by A and B is 27. Hence we get two equations in two variables which we can solve to find speed of A and B.

Complete step by step answer:
Now let us say there are two persons A and B.
Now we know that they are 27km apart.
Now let us say they meet at point C.

Now we know if they walk in same direction they meet after 9 hours
Let the speed of A be x and B be y.
Hence the distance travelled by A is 9x and distance travelled by B is 9y.
Now we know that A has travelled 27km more than B hence we get
9x + 27 = 9y
Dividing the equation by 9 we get
x + 3 = y……………………(1)
Now consider the case where they travel in opposite directions.
Now again let us say they meet at point D.

Now we know that they meet in 3 hours.
Hence distance travelled by A is 3x and the distance travelled by B is 3y.
Now since they were 27km apart. 3x + 3y = 27
Dividing by 3 we get x + y = 9
Substituting the value of y from equation (1) we get
x + x + 3 = 9
Hence we get 2x = 6 which means x = 3.
Now substituting x = 3 in equation (1) we get y = x + 3 = 3 + 3 = 6.
Hence x = 3 and y = 6.

Hence speed of A is 3 km per hour and B is 6km per hour.

Note: Now here note that when they travel in opposite directions we need not consider the distance as negative as we are considering just the distance travelled and not the direction. Here we have that sum of the distance travelled by A and B is 27 km. Hence we do not consider direction.