Question

A takes 3 hours more than B to walk 30 km. But, if A doubles his pace, he is ahead of B by 11/ 2 hours. Find their speed of walking

• A. A's speed = 5km/hr, B's speed = 8 km/hr
• B. A's speed = 15/2km/hr, B's speed = 6 km/hr
• C. A's speed = 10/3km/hr, B's speed = 5 km/hr
• D. Data insufficient

Answer 1

The correct option is C A's speed = 10/3km/hr, B's speed = 5 km/hr

Let the speed of A and B be x km/hr and y km/hr

Time taken by A to cover 30km $\frac{30}{x}hrs$

Time taken by B to cover 30km $\frac{30}{y}hrs$

According to the question

$\Rightarrow \frac{30}{x}-\frac{30}{y}=3$

$\Rightarrow \frac{10}{x}-\frac{10}{y}=1...eq1$

If A double his pace then the speed of A is 2x km/hr

therefore time taken by A to cover the 30 = 30/2xhrs And time taken by B to cover the 30KM = 30/yhrs

Now according to the question

$\Rightarrow \frac{30}{y}-\frac{30}{2x}=\frac{3}{2}$

$\Rightarrow \frac{10}{y}-\frac{5}{x}=\frac{1}{2}$

$\Rightarrow -\frac{10}{x}+\frac{20}{y}=\mathrm{1...}eq2$

Now we assume $\frac{1}{x}=u$ and $\frac{1}{y}=v$

Putting the u and v in eq1 and eq 2 we get

$\Rightarrow 10u-10v=1...eq3$

$\Rightarrow -10u+20v=1...eq4$

Adding eq3 and eq4 we get

$\Rightarrow 10v=2$

$\Rightarrow v=\frac{2}{10}$

$\Rightarrow v=\frac{1}{5}=\frac{1}{y}$

$\to y=5$

$Putv=\frac{1}{5}ineq3$

$\Rightarrow 10u-3=0$

$\Rightarrow u=\frac{3}{10}=\frac{1}{x}$

$\Rightarrow x=\frac{10}{3}$

Hence, the speed of A = 10\3 km/hr

The speed of B=5 km/hr respectively