Question

Pranali and Prasad started walking to the east and to the north respectively from the same point and at the same speed. After $2$ hours, the distance between them was $15\sqrt 2$. Find their speed per hour.

Answer 1

Hint:
Assume the distance walked by Pranali and Prasad to be x. We will use Pythagoras theorem which states that “In a right-angled triangle, the sum of the square of the hypotenuse side is equal to the sum of squares of the two other sides”. This can also be written as- ${H^2} = {P^2} + {B^2}$ Where H is the hypotenuse, P is the perpendicular of the triangle and B is the base of the triangle. Find the value of x by putting the given values in the theorem. Then use the formula of speed which gives a relation between distance and time. Put the values in the formula and solve it.

Complete step by step solution:
Let the point be A from where Pranali walks to point B in the east direction and Prasad walks from A to point C in the north direction. According to the question, AB=AC= x km(let)
It is given that the distance between the points B and C is$15\sqrt 2 $km
Time= $2$ hrs
We have to find their speed.

From the given figure, we can see that the paths will form a right-angled triangle where AC is the perpendicular, BC is the hypotenuse and AB is the base of the triangle. So we can use Pythagoras theorem to find the value of x.
According to Pythagoras theorem, ${H^2} = {P^2} + {B^2}$ Where H is the hypotenuse, P is the perpendicular of the triangle, and B is the base of the triangle
$ \Rightarrow B{C^2} = A{C^2} + A{B^2}$
On putting the given values, we get-
$ \Rightarrow {\left( {15\sqrt 2 } \right)^2} = {x^2} + {x^2}$
On solving, we get-
$ \Rightarrow 225 \times 2 = 2{x^2}$
On further solving, we get-
$ \Rightarrow 225 = {x^2}$
On simplifying, we get-
$ \Rightarrow x = \sqrt {225} = 15$km
Now, we know that speed=$\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}$
On putting the given values in this formula, we get-
$ \Rightarrow $ Speed=$\dfrac{{15}}{2}{\text{kmph}}$
On solving, we get-
$ \Rightarrow $ Speed=$7.5{\text{ kmph}}$

The speed of Pranali and Prasad is $7.5$ Kmph.

Note:
While drawing the figure, make sure you are labeling it correctly. This means that if you draw the figure (I) then it is the wrong figure because in this figure, Pranali is walking towards the north and Prasad is walking towards the east which does not match the statement of the question.

In question, it is given that Pranali walks to the east and Prasad to the north as drawn in figure (II).