Question

A man travels from $A$ to $B$ at a speed of $x$ km/hr. He then rests at $B$ for $x$ hours. He then travels from $B$ to $C$ at a speed of $2x$ km/hr and rests for $2x$ hours. He moves further to $D$ at a speed twice as that between $B$ and $C$. He thus reaches $D$ in $16$ hours. If the distance $A-B,B-C,$ and $C-D$ are all equal to $12$ km, then what could be the time for which he rested at $B?$

• A. $x=3hrs$
• B. $x=\frac{7}{3}hrs$
• C. $x=\frac{5}{3}hrs$
• D. $x=2hrs$

Answer 1

Answer: (A), (B)

The correct options are
A $x=3hrs$
B $x=\frac{7}{3}hrs$

Total time taken from A to D $=\frac{12}{x}+x+\frac{12}{2x}+2x+\frac{12}{4x}$

$=\frac{48}{4x}+\frac{24}{4x}+\frac{12}{4x}+3x=\frac{21}{x}+3x$

Given $=\frac{21}{x}+3x=16$

$\Rightarrow 21+3x^2-16x=0$

$\Rightarrow 3x^2-16x+21=0$

$\Rightarrow 3x^2-9x-7x+21=0$

$\Rightarrow 3x(x-3)-7(x-3)=0$

$\Rightarrow (x-3)(3x-7)=0$

$\Rightarrow x=3orx=\frac{7}{3}$