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# Two Joggers

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Two runners run for 1 hour at a constant speed on a 400 m track: The first runs at 10 km/h, the second at 7 km/h. The 2 runners start together at the same point. How many times do they cross each other if they are running in opposite directions? Thank you for help.

Apr 25, 2022

#1
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10 km / h  =   10000m/ 60 min  = (500/3) m / min

7 km / h =  7000m  / 60 min   = (350/3)m/ min

(500 + 350)  / 3 =   850 / 3  =  the number of combined meters  they run every min

And   400  m  =    (  1200 /3   )  meters

So....every minute   they  run    ( 850  / 1200)  = 17/24  of a lap  combined

1 min =  17/24 lap

24/17 min  =  1 lap

So  they  will pass  each other every    24/17  min

So in  60 min  they will pass each other

integer 60 / [ 24 /17]    =  integer  [ 60 * 17 ] /  24   =   42 times   Apr 25, 2022
edited by CPhill  Apr 25, 2022
#2
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10,000 / 60 ==166 2/3 m/minute - speed of the faster runner
7,000 / 60 ==116 2/3 m/minute - speed of the slower runner.

166 2/3 + 116 2/3==283 1/3 m/minute - speed at which they are approaching each other.

400 m / 283 1/3 m/minute ==1.41176 - minutes after the start - when they will cross each other.
1 hour ==60 minutes - hence they will cross:

60 / 1.41176 ==42.5==42 times after which they will cross the finish line at the same time

Apr 25, 2022