At his usual speed a cyclist covers a certain distance in 8 hours. When the speed of cycle is increased by 4 km/hr the same distance can be covered in 6 hours. Find the distance.
Answer & explanation
Correct answer: option 3
Let the usual speed of the cyclist be $x\text{ km/h}$.
Then the increased speed is $x + 4\text{ km/h}$.
Since the distance is the same:
$8x = 6(x + 4)$
$8x = 6x + 24$
$2x = 24$
$x = 12\text{ km/h}$
Now, the distance is:
$\text{Distance} = \text{Speed} \times \text{Time} = 12 \times 8 = 96\text{ km}$