Question

If Laisha walks for 1 hour and cycles for 2 hours she can travel 33 km. But if she walks for 2 hours and cycles for 1 hour she can cover 24 km. What are her walking and cycling speeds?

Answer 1

Hint: Assume both her walking and cycling speeds to be some variables \[x\] and \[y\]. Form two different equations in \[x\] and \[y\] from the given two conditions using formula ${\text{Distance}} = {\text{Speed}} \times {\text{Time}}$. Solve these equations simultaneously to get the required speeds.

Complete step-by-step answer:
According to the question, two conditions are given to us based on the distance traveled by Laisha by walking and by cycling.
Let the walking and cycling speeds of Laisha are \[x\] km/hr and \[y\] km/hr respectively.
From the first condition, if Laisha walks for 1 hour and cycles for 2 hours she can travel 33 km. We know the speed-distance formula ${\text{Distance}} = {\text{Speed}} \times {\text{Time}}$. Applying this we’ll get:
$
   \Rightarrow x \times 1 + y \times 2 = 33 \\
   \Rightarrow x + 2y = 33{\text{ }}.....{\text{(1)}} \\
 $
Next condition is, if she walks for 2 hours and cycles for 1 hour she can cover 24 km. From this we’ll get:
$
   \Rightarrow x \times 2 + y \times 1 = 24 \\
   \Rightarrow 2x + y = 24{\text{ }}.....{\text{(2)}} \\
 $
So we have two equations (1) and (2).
Now, multiplying equation (2) by 2 and subtracting it from (1), we’ll get:
$
   \Rightarrow x + 2y - 2\left( {2x + y} \right) = 33 - 2\left( {24} \right) \\
   \Rightarrow x + 2y - 4x - 2y = 33 - 48 \\
   \Rightarrow - 3x = - 15 \\
   \Rightarrow x = 5 \\
 $
So the walking speed of Laisha is 5 km/hr. If we put $x = 5$ in equation (1), we’ll get:
$
   \Rightarrow 5 + 2y = 33 \\
   \Rightarrow 2y = 28 \\
   \Rightarrow y = 14 \\
 $

Thus the walking speed of Laisha is 5 km/hr and her cycling speed is 14 km/hr.

Note:
If a linear equation is having only one variable, it can be solved directly to get the value of the variable. If it is a two variable equation then to determine the values of two different variables, we need two different equations in those variables. Similarly if there are $n$ different variables then we require $n$ different equations to find their values.