Question

A man walks at $6km/h$ and runs at $8km/h$. He covers $6km$ in $50min$ partly by running and partly by walking.
(i) For how long did he walk?
(ii) What distance did he cover walking?

Answer 1

Walking speed = 6km/hr or $\frac{6km}{60min}$

Running speed = 8 km/hr or $\frac{8km}{60min}$

Total distance to cover $\Rightarrow 6km$

Total Time taken = 50 min

Let the distance covered while waking = (x)km

running = (6-8)

$\therefore$ according to ques :-

$\frac{x}{6/60}+\frac{6-x}{8/60}=50$

$\Rightarrow 60\times \frac{1}{2}[\frac{x}{3}+\frac{6-x}{4}]=50$

$\frac{4x+18-3x}{12}=\frac{5}{3}$

$1(x-18)=5\times 4$

$x=20-18\Rightarrow 2,$

$x=2$

$6-x=4$

$\therefore$ Now,

(ii) Distance covered while walking $\Rightarrow 2km$

(i) He walked for $\left(\frac{x}{6/60}\right)min\Rightarrow (\frac{2}{6}\times 60)$

$\Rightarrow \frac{60}{3}\Rightarrow 20min$