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Mathematics 68 Online
OpenStudy (anonymous):

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

OpenStudy (anonymous):

right so this is a bit harder to parse

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

so it's gone exactly 60 miles already

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

so 70T - 60T = 60 = 10T

OpenStudy (anonymous):

so 10T = 60

OpenStudy (anonymous):

In six hours, they would have traveled the same distance

OpenStudy (anonymous):

so now let's check this:

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

which is exactly the point the second train passes the first

OpenStudy (anonymous):

make sense?

OpenStudy (anonymous):

yep!!

OpenStudy (anonymous):

awesome =)

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