Time and Distance Practice Test 4 with solutions

Let speeds of A and B are ${\mathit{x}}_1$ and ${\mathit{x}}_2$ km/hr and times taken by them are ${\mathit{t}}_1$ and ${\mathit{t}}_2$ hrs, then
${\mathit{x}}_1+{\mathit{x}}_2$ = 7 km/hr ...(i)
${\mathit{t}}_1+{\mathit{t}}_2$ = 14 hrs ...(ii)
Now, $\frac{24}{{\mathit{x}}_1}+\frac{24}{{\mathit{x}}_3}$ = 14
⇒ $\frac{24\left({\mathit{x}}_1+{\mathit{x}}_2\right)}{{\mathit{x}}_1{\mathit{x}}_2}$ = 14
∴ ${\mathit{x}}_1{\mathit{x}}_2$ = $\frac{24\times 7}{14}$ = 12
Then, ${\mathit{x}}_1-{\mathit{x}}_2$ = $\sqrt{{\left({\mathit{x}}_1+{\mathit{x}}_2\right)}^2-4{\mathit{x}}_1{\mathit{x}}_2}$ = $\sqrt{{\left(7\right)}^2-4\times 12}$ = 1 ... (iii)
Solving (i) and (iii) we get ${\mathit{x}}_1$ = 4 km/hr