Answer

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Hint: Just take time as $\left( \dfrac{T}{60} \right)$ hours then find distance taken by each in terms of T and then add it and equate it to total jogging distance.

Complete step-by-step answer:

Let Deepak and his wife meet for the first time in \[{{\text{T}}_{\text{min}}}\].

So, T will be expressed in hours as \[\dfrac{T}{60}\].

The speed of Deepak is 4.5 km/hr. Converting the speed into meters per hour, we get Deepak’s speed as 4500 m/hr, because 1km=1000m.

We know speed is equal to distance by time, or $d=s\times t$.

Then, after time \[{{\text{T}}_{\text{min}}}\left( \text{or }\dfrac{T}{60}\text{hours} \right)\] the distance travelled by him is \[4500\times \dfrac{T}{60}\] hours.

The speed of Deepak’s wife is 3.75 km/hr, so we can write her speed as 3750 m/hr.

Then, after time \[{{\text{T}}_{\text{min}}}\left( \text{or }\dfrac{T}{60}\text{hours} \right)\] the distance travelled by her is $3750\times \dfrac{T}{60}$ hours.

Now the total distance that can be travelled is 726m, i.e., the circumference of the jogging track.

Total distance travelled by Deepak and his wife is $4500\times \dfrac{T}{60}+3750\times \dfrac{T}{60}$.

So, we can equate it as,

\[\begin{align}

& 4500\times \dfrac{T}{60}+3750\times \dfrac{T}{60}=726 \\

& \Rightarrow 450\dfrac{T}{6}+375\times \dfrac{T}{6}=726 \\

& \Rightarrow \dfrac{T}{6}(450+375)=726 \\

\end{align}\]

On simplifying we get,

\[\begin{align}

& \dfrac{T}{6}\times 825=726 \\

& \Rightarrow T=726\times \dfrac{6}{825} \\

\end{align}\]

Hence, Deepak and his wife will meet for the first time in 5.28 minutes.

Note: As they two move in opposite directions their speed will be added and as we know the total distance then we can apply time in equal to total distance divided by total time taken.

Students often make mistakes by subtracting the distance or speed.

Another approach is to first convert the distance of the jogging track in km. And next as the speeds are given we can add the speed to find out the total distance travelled per hour in km. Then multiply the obtained value with the circumference of the jogging track in km.

Complete step-by-step answer:

Let Deepak and his wife meet for the first time in \[{{\text{T}}_{\text{min}}}\].

So, T will be expressed in hours as \[\dfrac{T}{60}\].

The speed of Deepak is 4.5 km/hr. Converting the speed into meters per hour, we get Deepak’s speed as 4500 m/hr, because 1km=1000m.

We know speed is equal to distance by time, or $d=s\times t$.

Then, after time \[{{\text{T}}_{\text{min}}}\left( \text{or }\dfrac{T}{60}\text{hours} \right)\] the distance travelled by him is \[4500\times \dfrac{T}{60}\] hours.

The speed of Deepak’s wife is 3.75 km/hr, so we can write her speed as 3750 m/hr.

Then, after time \[{{\text{T}}_{\text{min}}}\left( \text{or }\dfrac{T}{60}\text{hours} \right)\] the distance travelled by her is $3750\times \dfrac{T}{60}$ hours.

Now the total distance that can be travelled is 726m, i.e., the circumference of the jogging track.

Total distance travelled by Deepak and his wife is $4500\times \dfrac{T}{60}+3750\times \dfrac{T}{60}$.

So, we can equate it as,

\[\begin{align}

& 4500\times \dfrac{T}{60}+3750\times \dfrac{T}{60}=726 \\

& \Rightarrow 450\dfrac{T}{6}+375\times \dfrac{T}{6}=726 \\

& \Rightarrow \dfrac{T}{6}(450+375)=726 \\

\end{align}\]

On simplifying we get,

\[\begin{align}

& \dfrac{T}{6}\times 825=726 \\

& \Rightarrow T=726\times \dfrac{6}{825} \\

\end{align}\]

Hence, Deepak and his wife will meet for the first time in 5.28 minutes.

Note: As they two move in opposite directions their speed will be added and as we know the total distance then we can apply time in equal to total distance divided by total time taken.

Students often make mistakes by subtracting the distance or speed.

Another approach is to first convert the distance of the jogging track in km. And next as the speeds are given we can add the speed to find out the total distance travelled per hour in km. Then multiply the obtained value with the circumference of the jogging track in km.

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