Question

Mary cycles at 6km per hour. How long will she take to reach her Aunty's house, which is 12km away? If she cycles at the Speed of 4km/hr, how long will she take?

Answer 1

$\Large{\underbrace{\frak{\purple{Required \; Answers:}}}}$

$\begin{array}{|c|c|c|} \cline{1-3} \pink{\bf Speed }& \pink{\bf {Distance}} & \pink{\bf {Time}} \\\dfrac{\qquad\qquad\qquad\qquad}{} & \dfrac{\qquad\qquad\qquad\qquad}{} & \dfrac{\qquad\qquad\qquad\qquad}{} \\ \sf 6 km/hr & \sf{12\;km} & \sf{?} \\&\\ \sf 4km/hr & \sf {12\;km} & \sf{?} \\\cline{1-3}\end{array}$

 

❍ As we know that,

$\star \; \underline{\boxed{\sf{\purple{Speed = \dfrac{Distance}{Time}}}}}$

     

$\implies \sf{6 = \dfrac{12}{Time_1}}$

$\implies \sf{Time_1 = \dfrac{\cancel{12}}{\cancel{6}}}$

$\implies \underline{\boxed{\sf{\orange{Time_1 = 2 \; hours}}}}$

       

$\begin{array}{|c|c|} \cline {1-2} \pink{\bf{Speed}} & \pink{\bf {Time \; (hour)}} \\\dfrac{\qquad\qquad\qquad\qquad}{}&\dfrac{\qquad\qquad\qquad\qquad}{} \\\sf 6km/hr& \sf 12 \; km \\ &\\\sf 4km/hr & \sf{12 \; km} \\ \cline {1-2}\end{array}$

         

$\implies \sf{Speed \times Time = Constant}$

$\implies \sf{6 \times 2 =12}$

   

Let her take x hours to cover 12 km at the speed of 6 kilometers per hour & y hours to cover the same distance at 4 kilometers per hour.

   

$\begin{array}{ |c|c|c|} \cline{1-3} \pink{\bf Speed }& \pink{\bf {Time}} & \pink{\bf {Distance}} \\\dfrac{\qquad\qquad\qquad\qquad}{} & \dfrac{\qquad\qquad\qquad\qquad}{} & \dfrac{\qquad\qquad\qquad\qquad}{} \\ \sf 6 km/hr & \sf{x \; hours} & \sf{12 \; km} \\&\\ \sf 4km/hr & \sf {y \; hours} & \sf{12 \; km} \\ \cline{1-3}\end{array}$

   

Here, speed × Time = distance (constant)

   

$\implies \sf{6x = 12}$

$\implies \sf{x = \dfrac{\cancel{12}}{\cancel{6}} }$

$\implies \underline{\boxed{\sf{\orange{x = 2}}}}$

 

$\implies \sf{4y = 12}$

$\implies \sf{y = \dfrac{\cancel{12}}{\cancel{4}}}$

$\implies \underline{\boxed{\sf{\orange{y = 3}}}}$

   

⮩ Mary takes 2 hours at the speed of 6 kilometers per hour, & takes 3 hours at the speed of 4 kilometers per hour.

Answer 2

Answer:

Speed of the cycle = 6 km / hr

Distance travelled to reach her Aunt’s house = 12 km

∴ Time requried = (Distance travelled)/Speed

= 2 hours

Let the time required when the speed of the cycle is 4 k,/hr be x hours.

The speed of the cycle and the time required to the travel the same distance are in inverse proportion.

∴ 4 × x = 6 × 2

∴ x = (6 x 2)/4 = 3 hours

∴ Mary will require 2 hours if she is cycling at 6 km/hr and 3 hours if she is cycling at 4 km/hr to reach her Aunt’s house.