SOLUTION: priya climbs up 5 stairs every second and then climbs down 2 stairs over the next second how many second will she take to climb 60 Stairs

Question 1121087: priya climbs up 5 stairs every second and then climbs down 2 stairs over the next second how many second will she take to climb 60 Stairs
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
she climbs up 5 stairs the first second and climbs down 2 stairs the next second.

in two seconds, she has climbed up at a net rate of 3 stairs every 2 second interval.

60 stairs divided by 3 is equal to 20 intervals of 2 seconds each, 40 seconds total.

it's tempting to say that it would take her 40 seconds to climb 60 stairs, but this is not the case.

it actually takes her less seconds, because once she reaches 60 stairs she stops and then doesn't climb back down again.

if we back off 6 seconds, we might be able to find the stopping point when she reaches the 60 stairs.

at the end of 34 seconds, she has climbed up 17 * 5 and climbed down 17 * 2 for a net gain of 17*5 - 17*2 = 51 stairs.

in the 35th second she climbs up another 5 to get to 56
in the 36th second she climbs down another 2 to get to 54.

in the 37th second she climbs up another 5 to get to 59.
in the 38th second she climbs down another 2 to get to 57.

in the 39th second, she climbs up another 5 to get to 62.
she stops because she's already climbed up 60 stairs.

it took her 39 seconds to climb 60 stairs.

here's what the progression looks like second by second.

$$$

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