If a train leaves new york at 12am towards dc a 250mile trip going 70 and a train leaves dc at 2am headed to newyork going 40mph where would they collide

Question

What is the anwser and please tell me how you solbed it

Answer 1

Distance = rate x time

 

 

Distance traveled by the first train is 70 x T where T is the time

Distance traveled by the second train is 40 x t where t is the time.

They collide when they travel 250 miles altogether.

 

250 = 70*T + 40(t-2)

 

250 = 70T + 40T - 80 <--- distributive

 

250 = 110T - 80  <--- combines like terms

 

330 = 110T  <--- adds 80 to both sides

 

T = 330/110 = 3  <--- solves for T

 

The trains travel a total of 250 miles after three hours.

 

They collide at 3 am.

When they collide, they will be 40 miles from DC, as the second train will have only traveled 1 hour.

 

Here's the timeline....

 

                                    1st Train                                    2nd Train            

 

  12 am                         leaves NY                                 still in DC

 

   1 am                        70 miles from NY;                       still in DC

                                   180 miles from DC

 

   2 am                     140 miles from NY;                       leaves DC

                                   110 miles from DC;

 

   3 am                      210 miles from NY;                      40 miles from DC  <---- collision

                                  40 miles from DC