A frog is in a 40m deep place. Each day, the frog climbs 3m, but falls back 1m at night. How many days will it take to get out?

Calculate Net Distance: Identify the net distance the frog climbs each day. During the day, the frog climbs 3m, but at night it falls back 1m, so the net distance climbed each day is 3m - 1m = 2m.Calculate Last Day Climb: Calculate the distance the frog will climb on the last day. Since the frog climbs 2m net each day, it will reach a point where it can climb out without falling back. This will happen when the frog is within 3m of the top, since it can climb out in one go without falling back that night.Determine Remaining Climb: Determine the distance the frog needs to climb before the last day. The frog needs to climb 40m in total. If it can climb out from a point 3m below the top, it needs to climb 40m - 3m = 37m before the last day.Calculate Days to Climb: Calculate the number of days it will take to climb 37m with a net climb of 2m per day. To find the number of days, divide the distance by the net climb per day: 37m / 2m per day = 18.5 days. Since the frog cannot climb half a day, it will complete the 37m in 19 days.Add Last Day: Add the last day to the total number of days. The frog will climb out on the 20th day, as it will not fall back that night. So, the total number of days is 19 days + 1 day = 20 days.

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A frog is in a $40\,\text{m}$ deep place. Each day, the frog climbs $3\,\text{m}$ , but falls back $1\,\text{m}$ at night. How many days will it take to get out?

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Q. A frog is in a

40\,\text{m}

deep place. Each day, the frog climbs

3\,\text{m}

, but falls back

1\,\text{m}

at night. How many days will it take to get out?

Calculate Net Distance: Identify the net distance the frog climbs each day. During the day, the frog climbs $3\,\text{m}$ , but at night it falls back $1\,\text{m}$ , so the net distance climbed each day is $3\,\text{m} - 1\,\text{m} = 2\,\text{m}$ .
Calculate Last Day Climb: Calculate the distance the frog will climb on the last day. $\newline$ Since the frog climbs $2\,\text{m}$ net each day, it will reach a point where it can climb out without falling back. This will happen when the frog is within $3\,\text{m}$ of the top, since it can climb out in one go without falling back that night.
Determine Remaining Climb: Determine the distance the frog needs to climb before the last day. $\newline$ The frog needs to climb $40\,\text{m}$ in total. If it can climb out from a point $3\,\text{m}$ below the top, it needs to climb $40\,\text{m} - 3\,\text{m} = 37\,\text{m}$ before the last day.
Calculate Days to Climb: Calculate the number of days it will take to climb $37\,\text{m}$ with a net climb of $2\,\text{m}$ per day. $\newline$ To find the number of days, divide the distance by the net climb per day: $\frac{37\,\text{m}}{2\,\text{m} \text{ per day}} = 18.5$ days. Since the frog cannot climb half a day, it will complete the $37\,\text{m}$ in $19$ days.
Add Last Day: Add the last day to the total number of days. $\newline$ The frog will climb out on the $20$ th day, as it will not fall back that night. So, the total number of days is $19$ days $+$ $1$ day $= 20$ days.