Question

Suppose you walk from home to the bus stand at $4km/h$ and immediately return at $xkm/hr$. If the average speed is $6km/hr$ then $x$ is

• A. $8km/hr$
• B. $10km/hr$
• C. $12km/hr$
• D. Cannot be determined unless the distance from home to bus stand is known

Answer 1

Answer: (C)

Step 1: Given data

Going speed = 4 km/h

Returning speed = x km/h

Average speed = 6 km/h

Let s be distance.

Step 2: Formula used

$Time=\frac{Distance}{Speed}$

$Averagespeed=\frac{Totaldistancetraveled}{Totaltimetaken}$

Step 3: Finding the value of x

$Time=\frac{Distance}{Speed}$

So, Total time = $\frac{S}{4}+\frac{S}{x}$

$Averagespeed=\frac{Totaldistancetraveled}{Totaltimetaken}$

Putting all the values

$6=\frac{s+s}{\frac{s}{4}+\frac{s}{x}}$
$6=\frac{8x}{x+4}$

x = 12 km/h

⇒3= 4xx+4⇒3x+12=4x⇒x=12 km/h\Rightarrow \quad 3 = \displaystyle\frac{4x}{x+4} \Rightarrow 3x + 12 = 4x \Rightarrow x = 12\space km/h

Hence the value of x is 12 km/h, and option C is correct.