SOLUTION: Dalton boards an elevator in the lobby that is headed up at 160 meters per minute. Meanwhile, 160 meters above, Kristen boards an adjacent elevator headed down at 150 meters per mi

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Question 1012856: Dalton boards an elevator in the lobby that is headed up at 160 meters per minute. Meanwhile, 160 meters above, Kristen boards an adjacent elevator headed down at 150 meters per minute. How long will it be before Dalton and Kristen pass each other?
Found 2 solutions by Theo, macston:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the total distance is 160 meters.
rate * time = distance.

the total distance they will have both traveled is 160 meters.

they will pass each other somewhere in the middle.

therefore the distance he travels plus the distance she travels is equal to 160 meters.

if he travels d meters, then she will have traveled 160 - d meters when they pass each other.

the number of minutes that each travels will always be the same.

therefore, when they meet, he will have traveled m minutes and she will have traveled m minutes as well.

the rate * time = distance formula applies.

for him:

rate * time = distance becomes 160 * m = d

for her:

rate * time = distance becomes 150 * m = 160 - d

since m and d have to be the same value in both equations, then these two equations need to be solved simultaneously.

you get:

160 * m = d
150 * m = 160 - d

replace d with its equivalent value of 160 * m in the second equation to get:

150 * m = 160 - (160 * m)

add 160 * m to both sides of this equation to get:

310 * m = 160

divide both sides of this equation by 310 to get m = 160/310.

this is equal to .516129... minutes.

in that many minutes, he will have traveled 82.58064516 meters at 160 meters per minute.

she will have traveled 77.41935484 meters at 150 meters per minute.

add those up and they equal 160 meters.

they will pass each other when both have traveled .51613 minutes rounded to 4 decimal places.

that's approximately 30.97 seconds rounded to 2 decimal places.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
x=time until they pass
.
(160m/min)x+(150m/min)x=160m
(310m/min)x=160m
x=160m/(310m/min)
x=16/31 min
.
(16/31 min)((60sec)/min)=30.97 seconds
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ANSWER: They will pass in 30.97 seconds (16/31 minutes).
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