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.
+128474 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
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
