A train leaves the station at 10:00 and travels due south at a speed of 60km/h. Another train has been heading due west at 45 km/h and reaches the same station at 11:00. At what time were the two closest together?
totally stuck on this one.
Ok, can you or someone check my work below because I can't seem to get the answer with the back.
I said..
Let x be the distance between A and B in km
Let a and b be the distance travelled by A and B in km
Min x at t=?
V=d/t
For A
a=60t
For B
b=45t
b^2+a^2=x^2
(45t)^2+(60t)^2=x^2
x=(5625t^2)^0.5
x'=5625t/[(5625t^2)^0.5]
x'=0 when t=0
domain of t
10<=t<=11
x(10)=750 km
x(11)=825 km
therefore the min distance between train A and train B is 750 km at 10:00
BUT>>> the back of the book's answer is: t=0.36 h
How do i get this and what did I do wrong?
the distances, and are measured from the origin.
the first train starts at the origin and moves away from the origin at 60 km/hr
the second train started 45 km away from the origin, and heads back toward the origin at 45 km/hr.
you see, after 1 hr, km from the origin. it made it back.