There is a escalator and 2 persons move down it.A takes 50 steps and B takes 75 steps while the escalator is m

Question

There is a escalator and 2 persons move down it.A takes 50 steps and B takes 75 steps while the escalator is moving down.Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps.Find the no. of steps in the escalator while it is staionary

Answer 1

it's 100 steps man....
A assume takes 1 step in 1 sec
so B takes 3 steps in 1 sec
and hence he comes down in 25 sec(75/3 sec)
and A comes down in 50 sec(50/1)
the no of steps is a constant, the difference between B and A is 25 seconds and 25 steps.... Hence the escalator moves at the rate of 1 step/sec.... So in 50 secs A climbs down 50 steps and the escalator another 50 so totally 100....Similarly B climbs down 75 steps in 25 sec by the time escalator would have moved 25 steps and totally 100....
Thanks for a good question after a very long time here.. I look forward to more like this

Answer 2

first 75 is the lower limit ie there are more than that because it is moving down there for making each step less since as it goes down you dont have to step down to get that distance achieved.

Totalsteps =T
EscaltorstepsremovedatBpace = R

T = 50 + 3R
T = 75 + R

75 + R = 50 + 3R
simplfy
by subtract 50 both sides

(75 - 50) + R = (50 - 50 ) + 3R
25 + R = 3R
simplfy subtract R each side
25 (R-R) = 3R - R
25 = 2R
simplfy divide by 2 each side
25/2 = 2R/ 2
12 1/2 = R

so that pluging back in either equation you get
T = 50 + 3(12 1/2) simplfy convert 12 1/2 to fraction
T = 50 + 3 ( 12 *2/2 + 1/2)
T = 50 + 3 (24/2 + 1/2)
T = 50 + 3(25/2) simplfy multiply 3 times 25/2
T = 50 + 75/2 simplfy convert 50 to fraction and add
T = 50* (2/2) + 75/2
T= 100/2 + 75/2
T = 175/2 simplfy divide by two
T = 87 1/2
check other equation
T = 75 + (25/2) simplfy convert 75 to fraction and add
T = 75 * (2/2) + 25/2
T = 150/ 2 + 25/2
T= 175/2 simplfy divide by two

T = 87 1/2 both equations check out there fore I have more confidence in claiming the answer is correct being that I set the equation up correctly. correct my errors