SOLUTION: The first train started eastwards at 40mph. One hour later, the second train starts southwards at 60mph. How fast in mph, are the two trains separating 2 hours after the start of t

Algebra ->  Test -> SOLUTION: The first train started eastwards at 40mph. One hour later, the second train starts southwards at 60mph. How fast in mph, are the two trains separating 2 hours after the start of t      Log On


   

Question 1149914: The first train started eastwards at 40mph. One hour later, the second train starts southwards at 60mph. How fast in mph, are the two trains separating 2 hours after the start of the 2nd train?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
draw this.
train 1 is 80 miles along the x-axis and d train 1/dt=40 mph
train 2 is 60 miles south on the y-axis and d train 2/dt=60 mph
s^2=train1^2+train2^2
differentiate
2s ds/dt=2 train 1 d train 1/dt+2train 2 * d train 2/dt
remove the 2s, since they divide out
s is 100 miles apart since it is a 60-80-100 right triangle
100*ds/dt=80*40+60*60=5200
ds/dt=52 mi/hr.

Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let "t" be the time after second train started.


The we have for distances from the starting point


    First train :  x(t) = 40 + 40*t

    Second train : y(t) = 60*t


The distance between the trains is  z(t) = sqrt%28%28x%28t%29%29%5E2%2B+%28y%28t%29%29%5E2%29 = sqrt%28%2840%2B40%2At%29%5E2+%2B+%2860%2At%29%5E2%29


The rate of separating, which the problem is asking about, is


    %28dz%29%2F%28dt%29 =  


Now substitute  t= 2 hours into the last formula and calculate


    %28dz%29%2F%28dt%29 =  = %281%2F2%29%2A%2824000%2Fsqrt%2828800%29%29 = 70.711 km/h.    ANSWER