SOLUTION: a train is going to a place B and the velocity is 80 km/h. After half an hour, another train leaves for B and its velocity is 100 km/h. both trains arrive in B at the same time. wh

Question 387634: a train is going to a place B and the velocity is 80 km/h. After half an hour, another train leaves for B and its velocity is 100 km/h. both trains arrive in B at the same time. what is the lengh of the route ?
Please tell me if this solution is good enough!
S1: speed of train 1
S2: speed of train 2
D1 = distance travelled by train 1
D2 = distance travelled by train 2
t1 : time it took train 1 to get at B
t2 : time it took train 2(which was late by 1/2 h) to get at B
When both trains arrive at place B, they would have travelled the same distance and thus: D1 = D2
S1 * t1 = S2 * t2
80 * t1 = 100 * (t1 - 1/2)
80t1 = 100t1 - 50
t1 = 2.5 hours
so the D1 = 80 * 2.5 = 200 km
also D2 = 100 * (2.5 - 0.5) = 200 km
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!

Your answer of 200 km is correct!
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Let x = time it takes for 80km/hr train to get to B
then
x- 1/2 = time it takes for 100km/hr train to get to B
80x = 100(x-1/2)
multiplying both sides by 2:
160x = 100(2x-1)
160x = 200x-100
0 = 40x-100
100 = 40x
100/40 = x
5/2 hours = x
Distance then is:
80(5/2) = 40*5 = 200 km

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