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27 September, 06:31

A frog is at the bottom of a 17-foot well. Each time the frog leaps, it moves up 3 feet. If the frog has not reached the top of the well, then the frog slides back 1 foot before it is ready to make another leap. How many leaps will the frog need to escape the well?

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  1. 27 September, 07:28
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    The frog takes 8 jumps to reach top of well

    Explanation:

    Given data

    Frog at bottom=17 foot

    Each time frog leaps 3 feet

    Frog has not reached the top of the well, then the frog slides back 1 foot

    To Find

    Total number of leaps the frog needed to escape from well

    Solution

    in 1 jump distance jumped=3 + (-1)

    =2 feet

    =2*1 feet

    The "-1" is because the frog goes back

    Now After 2 jumps the distance jumped as:

    Distance Jumped=2+2

    Distance Jumped=2*2

    =4 feet

    Similarly after 7 jumps

    Distance Jumped=2+2 + ... + 2

    Distance Jumped=2*7

    =14 feet

    Now after 8th jump the frog climbs but doesnot slide back as it is reached to the top of well.

    So

    Distance Jumped = (Distance Jumped after 7 jumps) + 3

    =14+3

    =17 feet

    The frog takes 8 jumps to reach top of well
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