Question

An explorer can scale 3 meters up a mountain slope in 1 minute. However, as the slope is highly slippery, after each minute of climbing, she slips down 2 meters. If each slip takes up a minute of her time, when will she step on the peak 18 meters above her?

• A. Between 32 and 33 minutes
• B. Between 33 and 34 minutes
• C. Between 34 and 35 minutes
• D. Between 35 and 36 minutes

Answer 1

The correct option is C Between 34 and 35 minutes

$\text{Distance climbed in the first minute}=3m$
$\text{Distance slipped down in the second minute}=2m$

$\therefore \text{Distance climbed in every 2 minutes}=3m-2m=1m$

$⟹\text{Time taken to climb}18m$
$=18\times \text{Time taken to climb}1m$
$=18\times 2minutes$
$=36minutes$

$\text{However, this time includes the last one}\text{minute she spends slipping down 2 m.}$

$\text{Hence, in the 35th minute, the explorer will}\text{be 2 m}above\text{the 18 m mark, at}\text{20 m.}$

$\text{Similarly, in the 34th minute, she will be}\text{3 m}below\text{the 20 m mark, at 17 m.}$

$\therefore \text{The explorer would step on the peak}$ $\text{18 m above her, sometime between}\text{34 and 35 minutes.}$