Question

Sita and Gita start walking from the same point on the road but in opposite directions. If Sita walks at the speed of 5 \[km/hr\] and Gita at the speed of 4 \[km/hr\], in how much time will they be 27 Km apart?

Answer 1

Hint: We use the formula of speed to write the formula of distance in terms of speed and time. Assume the time taken for them to be given distance apart as a variable and form equations of distance covered in that time for both Sita and Gita using the distance formula. Form an equation stating the distances obtained have sum equal to given distance apart.
* If ‘d’ distance is covered in time ‘t’, then speed ‘s’ is given by \[s = \dfrac{d}{t}\]

Complete step-by-step solution:
Let speed at which Sita is walking be \[{s_1}\]and speed at which Gita is walking be \[{s_2}\]
\[ \Rightarrow {s_1} = 5;{s_2} = 4\]
Since, we know speed is given by the formula \[s = \dfrac{d}{t}\]
Then by cross multiplying the values
\[ \Rightarrow d = st\]..................(1)
Let distance travelled by Sita be \[{d_1}\] and distance travelled by Gita be \[{d_2}\]: Then \[{d_1} + {d_2} = D\]..............… (2)
Where, D is the total distance between Sita and Gita i.e. \[D = 27\]
Let us assume that the time in which Sita and Gita will be 27 Km apart be ‘t’ hours.
Then from equation (1) we can write distance travelled by Sita and Gita in ‘t’ hours.
Distance travelled by Sita in ‘t’ hours \[{d_1} = {s_1}t\]
Substitute the value of \[{s_1} = 5\]
\[ \Rightarrow \]Distance travelled by Sita in ‘t’ hours \[{d_1} = 5t\]...............… (3)
Distance travelled by Gita in ‘t’ hours \[{d_2} = {s_2}t\]
Substitute the value of \[{s_2} = 4\]
\[ \Rightarrow \]Distance travelled by Gita in ‘t’ hours \[{d_2} = 4t\]................… (4)
Substitute the values of distances from equations (3) and (4) in equation (2)
\[ \Rightarrow 5t + 4t = 27\]
Add terms in LHS with same variable
\[ \Rightarrow 9t = 27\]
Divide both sides of the equation by 9
\[ \Rightarrow \dfrac{{9t}}{9} = \dfrac{{27}}{9}\]
Cancel same factors from numerator and denominator on both sides of the equation
\[ \Rightarrow t = 3\]

\[\therefore \]Time taken for Sita and Gita to be 27 Km apart is 3 hours

Note: Many students make mistake of making equations from the formula in terms of time as the question is demanding for value of time; they make equations for time taken by Sita and Gita which is wrong as we don’t have particular distances covered by each of them in their respective directions. Keep in mind we make equations for that variable whose complete value (in this case distance) is given to us.