train traveling north @ 60mph. one hour later, another train leaves @ 70mph. how far away before second train catches up? t

right so this is a bit harder to parse

so basically the second train has caught up once the distances they've traveled are exactly equal

ok so in one hour, once the second train leaves, the first train has a 60mph*1hr head start

so it's gone exactly 60 miles already

so from that point on, we're basically solving for some time T

70*T - 60*T = 60 (the head start being 60mph)

or in time T, when they have traveled the same distance, we know that 70*T = 60 + 60T

so 70T - 60T = 60 = 10T

so 10T = 60

In six hours, they would have traveled the same distance

so now let's check this:

In 6 hours from the original 1 hour, the first train has traveled 7hours

so it's traveled 7 hours * 60mp/h = 420 miles

the second train has traveled 6 hours total. so 6 hours * 70mph = 420miles

which is exactly the point the second train passes the first

make sense?

yep!!

awesome =)