maths problem?

Question

ok i don't expect that many answers here as no one is gonna want to do my homework for me, but here goes:


2 trains leave a destination, one 3 hours before the other. the one which leaves first goes at 35kilometres an hour and the other, at 50 km/hour. they are both going to the same place. at what distance from the place where they left will they meet.

the answer is 350km, but how do i reach that conclusion?

Answer 1

x is distance
t is time

x=50t This is for the second train.
x=35(t+3) This is for the first train.

50t=35t+105
50t-35t=105
15t=105
t=7 hours
x=50*7=350 km.

or x=35(7+3)=350 km.

Answer 2

Assume they meet at a distance of "x" kilo meters and travel time of second train is "t" hours.

So since first one's speed is 35, time taken is t + 3, then the distance of first train = 35 * (t + 3)
similarly speed of second one is 50 and time taken is t, then the distance of second train = 50 * t
Since they meet at a point then the distance travelled by both people should be equal;
so 35 * (t + 3) = 50 * t
35*t + 105 = 50*t
105 = 50t - 35t
15t = 105
t = 105/15
then the distance = 50*t
ie = 50 * 105 / 15
= 350 km
just try ;

you should get the same answer by
distance = 35 (t +3)
= 35 * 105/15 + 35 * 3
= 7 * 35 + 105
= 245 + 105
= 350 km

Ther you are ////////////////////////////////

Answer 3

You find the least common multiple of each "train" (or number).

ie:
multiples of 35 are: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350, and 385
multiples of 50 are: 50, 100, 150, 200, 250, 300, 350, 400.

The reasoning behind this step is after 1 hour, the first train has travelled 35 KM, after 2 hours--70, after 3 hours--105, etc. Same rule applies to the second train.

350 is your least common multiple. So the trains will meet at 350 KM.

Answer 4

in 3 hours the first train would have gained a lead of 35*3=105 km
this distance has to be closed before they meet
timetaken=distance to be closed/relative speed
relative speed=50-35=15 kmph
time taken after the second train starts=105/15=7 hours
in 7 hours the diatance travelled=50*7=350 km.

Answer 5

Let's call t0 the 3hrs in front, t1 the run time of the second train.
The time they meet will be t0 + t1. Let's call e the total distance (what we want to know).
Total distance (from base) run by the first train:
e = v1 * (t0 + t1)
By the second:
e = v2 * t1
Equal the two (so they meet):
v1 * (t0 + t1) = v2 * t1
v1.t0 + v1.t1 = v2*t1
35*3 + 35*t1 = 50*t1
15*t1 = 105
t1 = 7h
But t1 is the run of the second train, running at 50kph
So, distance e = v.t = 50 * 7 = 350km.