Question

Walking at three-fourths of his usual speed a man covers a certain distance in two hours more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with his usual speed is _________.

• A. $4.5$ hours
• B. $5.5$ hours
• C. $6$ hours
• D. $5$ hours

Answer 1

Answer: (C)

$6$ hours

Let the original speed be $x$

Let the original time taken be $y$

$\Rightarrow$ Distance Covered $=xy$

New Speed $=0.75x$

New Time Taken $=y+2$

$\Rightarrow$ Distance Covered $=0.75x(y+2)=0.75xy+1.5x$

$\Rightarrow xy=0.75xy+1.5x$

$\Rightarrow 0.25xy=1.5x$

$\Rightarrow y=\frac{1.5}{0.25}=6$