Math equation needed

Question

frog is in well 78 meters deep. He jumps 4 feet each day, when he sleeps he loses 2 meters. How many days will it take him to get to the top / basic equation?

Answer 1

For the equation as written, Mark is correct.  The frog never gets out.

 

Each day the frog jumps 4 ft

The conversion for ft to meters is 1:0.3048

 

4 ft = 4(.3048) = 1.2192 meters

 

If the frog goes up 1.2192m per day then loses 2m per day

he has an aggregate loss 0f .7808m per day and never gets out.

 

The other answers are assuming a typographical error in your problem

Answer 2

"He jumps 4 feet each day, when he sleeps he loses 2 meters."

 

Converting to same units:

 

He jumps 4 feet each day, when he sleeps he loses 6.56096 feet.

 

Poor frog, he never gets out!

Answer 3

I disagree that the answer is 39.

 

At the end of 37 days the frog is at the 74 meter mark. Therefore on the 38th day he goes four more meters and is at the top.

Answer 4

the frog is in the well 78 m deep

every day he gains 4 m and loses 2 m for a net gain of 2 m each day

78/2=39 days to get to the top

Answer 5

Hi Patrick,

 

This is an algebra problem.  As with all word problems, though, it's important to translate the words accurately into an equation.  

 

I see that you have mixed units for distance, feet and meters.  Because you mention meters twice I'm guessing "feet" was just a typo and will solve below for meters.  If not, you would convert the feet into meters:  4 feet = 1.22 meters; this would mean that the frog is actually losing more at night than he gains during the day, and so he'd never reach the top.  Poor froggie.

 

Anyway:  

 

Let d = total distance of travel in meters

Let V = rate in meters per day

Let t = time in days

 

We know that V = d / t, but we're solving for time, so we can rewrite the equation as t = d / V.  Now we just have to plug in the numbers.

 

1)  t = 78 meters / V

2)  V is a little trickier, because even though the frog gains 4 meters / day, he loses 2 meters / day (when he sleeps), so his net V is 2 meters / day

3)  So t = 78 meters / 2 meters / day

4)  t = ( 78 m/ 1) * (1 day / 2 meters)

5)  t = 39 days 

 

That's it!

 

Evan