Question

Out of $$900$$ km distance Indira travelled some distance by bus at the speed $$60$$ km/hr and the remaining by railway at the speed of $$90$$ km/hr. Totally she travelled for $$13$$ hrs. Find the distance travelled by the bus.

Answer 1

$$\textbf{Step 1: Using given constraints for travelling by bus and railway .}$$

$$\text{Let the distance travelled by bus be "x" km and by railway be "}$$ $$\mathrm{y}$$ $$\mathrm{km}$$.

$$\text{Total distance =900} \mathrm{~km}$$

$$\therefore
\mathrm{x}+\mathrm{y}=900 \ \ \ \ \ldots \ldots (i)$$

$$\text{Time
taken to travel by bus with a speed of 60} \mathrm{~km} /
\mathrm{hr}=[\mathrm{x} / 60] \mathrm{hr}$$

$$\text{Time
taken to travel by railway with a speed of 90} \mathrm{~km} /
\mathrm{hr}=[\mathrm{y} / 90] \mathrm{hr}$$

$$\text{Total
tlme taken for the complete Journey =13} \mathrm{hrs}$$

$$\therefore\dfrac{x}{60}+\dfrac{y}{90}=13$$

$$\Rightarrow
90 x+60 y=70200 \ \ \ \ldots . . . . (ii) $$

$$\textbf{Step 2: Solving given system of linear equations.}$$

$$\text{Now, multiplying by 90 throughout the eq. (i) and subtracting It eq. (II) from (1), we get}$$

$$90 x+90
y=81000$$

$$90 x+60
y=70200$$

$$30
\mathrm{y}=10800$$

$$\therefore
\mathrm{y}=\mathbf{3 6 0 \mathrm { km }}$$

$$\text{And,}$$

$$x=900-360=540 \mathrm{~km}$$

$$\textbf{Hence, the distance travelled by bus is 540} \boldsymbol{~km} .$$