Question

A man covers 1 mile in the first 5 minutes, half a mile in the next 5 minutes, and a fourth of a mile in the 5 minutes after that on his morning run. If he continues in this pattern, how long would he take to cover 2 miles?

• A. 20 minutes
• B. 30 minutes
• C. 1 hour
• D. Infinity

Answer 1

The correct option is D Infinity

Following the pattern, we find that the distance covered in each 5 minutes is halved.

Hence, the total distance covered in the first 15 minutes would be:

$1mi+\frac{1}{2}mi+\frac{1}{4}mi$

Similarly, the total distance covered after an inifinite time will be the sum of the infinite series:

$D=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....$

Subtracting 1 from both sides, we get:

$⟹D–1=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....$

Also, dividing the sum 'D' by 2, we get:

$\frac{D}{2}=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+....$

$⟹\frac{D}{2}=D–1$

$⟹\frac{D}{2}=1$

$⟹D=2mi$

Hence, the runner would be able to cover 2 miles in an inifinitely long time.