distane getween trains is 450 km.
one train travels 100 km / hr.
other train travels 50 km / hr.
they will meet when the total distance traveled by both of them is equal to 450 km.
equation for distance is R*T = D.
This means that rate * time = distance.
We know the rates.
We know the distance.
We know that the time that each train travels will be the same.
We let h = the time each train travels.
train 1 travels 100 km / hr * h hours.
train 2 travels 50 km / hr * h hours.
the total distance they travel is 450 km.
our equation is:
100 * h + 50 * h = 450
combine like terms to get:
150 * h = 450
divide both sides by 50 to get:
h = 450/150 = 3
They will meet in 3 hours.
train 1 will have traveled 100 * 3 = 300 km.
train 2 will have traveled 50 * 3 = 150 km.
total distance traveled by both trains is equal to 450 km.
the bird was flying at 200 km/h.
in the same 3 hours the bird flew a total of 200 * 3 = 600 km.
bird flies 450 km in one direction, then travels back 150 km when the trains meet.
450 + 150 = 600 km.
if the bird started at the end of the faster train, the bird will be directly overhead when the trains meet.
if the bird started at the end of the slower train, the bird will not be anywhere near the trains when they meet.
here's what it looks like:
each > equals 10 km distance traveled towards the right.
each < equals 10 km distance traveled towards the left.
fast train (FT) travels 300 km.
slow train (ST) travels 150 km.
total distance traveled by both trains = 450 km.
each train traveled for 3 hours.
FT|>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>|
|<<<<<<<<<<<<<<< ST
| |
trains meet here|
if the bird started on the left end:
B |>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>|>>>>>>>>>>>>>>>|
|<<<<<<<<<<<<<<<|
|
bird travels 600 km to here|
if the bird started on the right end:
|<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<|<<<<<<<<<<<<<<<| B
|>>>>>>>>>>>>>>>|
|
bird travels 600|
km to here|