Question

A boy covers a distance of 20 km in 5/2 hrs, partly on foot at the rate of 5km/hr and partly on bicycle at the rate of 10km/hr. Find the distance covered on foot.​

Answer 1

Answer:

Here, the concept of distance, time and speed relationship has been used. We see that we're given with the total distance covered by a boy, total time taken to cover the distance and speed of the boy to cover the distance (on foot) partly on the foot and partly on bicycle. Also, the speed of bicycle is given. We're asked to calculate the distance covered by the boy on foot. So, firstly we've to calculate the total speed of the boy to cover the total distance taking distance covered by the boy on foot as variable and after further solving we'll get the answer.

Formula used:

$\bullet\quad\boxed{\sf{Speed=}\; \bold{\dfrac{Distance}{Time}}}$

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Solution:

Given,

» Total distance covered by the boy = d = 20 km/hr

» Total time taken = t = 5/2 hrs

~ For the total speed of the boy ::

We know that,

$\; \; \longrightarrow\quad\tt{Speed=\dfrac{Distance}{Time}}$

By applying the values in the formula, we get:

$\; \; \longrightarrow\quad\tt{Speed=\dfrac{20}{\left[\; \; \dfrac{5}{2}\; \; \right]}}$

$\; \; \longrightarrow\quad\tt{Speed=\dfrac{20\times 2}{5}}$

Performing multiplication.

$\; \; \longrightarrow\quad\tt{Speed=\dfrac{40}{5}}$

Performing division.

$\; \; \longrightarrow\quad\tt{Speed=\bold{8\; km/hr}}$

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~ For the distance covered by boy on foot ::

• Let the distance covered by boy on foot be x.

$\underline{\bigstar\;\boldsymbol{According\; to\; the\; question\; :}}$

• Total distance covered by the boy equals to 20 km. So,

>> The distance covered by boy on foot = x km

>> The distance covered by boy on bicycle = 20 - x km

Using formula, let's calculate time taken by the boy to cover the distance by foot.

$\; \; :\implies\quad\tt{Time\; taken=\dfrac{Distance}{Speed}}$

As we have assumed that the distance covered by boy on foot is x km and it is given in the qúestion that the speed of the boy to cover the distance by foot equals to 5 km/hr. Thus, writing it in the form of equation.

$\; \; :\implies\quad\tt{{Time\; taken}_{(Foot)}=\dfrac{x}{5}}$

Now, let's calculate the time taken by the boy to cover the distance by bicycle. $\\\; \; :\implies\quad\tt{{Time\; taken}_{(Bicycle)}=\dfrac{Distance}{Speed}}$

As per the provided information in the qúestion and our assumption, the distance covered by the boy on bicycle equals to 20 - x km and the speed of the boy to cover the distance on bicycle equals to 10 km/hr. Writing it in the form of equation.

$\; \; :\implies\quad\tt{{Time\; taken}_{(Bicycle)}=\dfrac{20-x}{10}}$

It is given in the qúestion that total time taken by the boy to cover the total distance is 5/2 hours. We know, sum of t1 and t2 equals to the total time taken. Here, t1 is the time taken by the boy to cover the distance by foot and t2 is the time taken by the boy to cover the distance by bicycle. So, $\\\; \; \longmapsto\quad\tt{Total\; time={Time\; taken}_{(Foot)}+{Time\; taken}_{(Bicycle)}}$

By applying the values in the formula, we get:

$\; \; \longmapsto\quad\tt{\dfrac{5}{2}=\dfrac{x}{5}+\dfrac{20-x}{10}}$

Multiplying 2 on both numerator and denominator.

$\; \; \longmapsto\quad\tt{\dfrac{5}{2}=\dfrac{2x}{10}+\dfrac{20-x}{10}}$

Performing addition between two fractions.

$\; \; \longmapsto\quad\tt{\dfrac{5}{2}=\dfrac{2x+20-x}{10}}$

Performing subtraction on numerator of RHS.

$\; \; \longmapsto\quad\tt{\dfrac{5}{2}=\dfrac{x+20}{10}}$

Transposing 10 from RHS to LHS. It's arithmetic operator will get change.

$\; \; \longmapsto\quad\tt{\dfrac{5\times 10}{2}=x+20}$

Performing multiplication in LHS (numerator).

$\; \; \longmapsto\quad\tt{\dfrac{50}{2}=x+20}$

Performing division in LHS.

$\; \; \longmapsto\quad\tt{25=x+20}$

Transposing 20 from RHS to LHS. It's sign will get change.

$\; \; \longmapsto\quad\tt{25-20=x}$

Performing subtraction in order to calculate the value of x.

$\; \; \longmapsto\quad\underline{\boxed{\tt{x}=\bold{\purple{5\; km}}}}$

Therefore, the required answer is:

❝ The distance covered by boy on foot is 5 km. ❞