.
P and Q are two stations. Train A started from P
towards Q at 6:00 a.m at 90 kmph. At the same
time, train B started from R, an intermediate station
60 km from P, and travelled towards Q at 60 kmph.
Train C started from Q towards P at 7:00 a.m at
120 kmph. All the trains crossed each other
simultaneously. Find PQ (in km)
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Let t be the time train A traveled to get the meeting point (in hours).
Then from the problem, train B traveled the same time t from R to get the meeting point;
train C traveled (t-1) hours from Q to get the meeting point.
Consider trains A and B.
To get the meeting point, train A traveled 90*t kilometers;
train B traveled 60*t kilometers.
For train B, the travel distance to get the meeting point was 60 km less than that for train A,
so we write this equation
90t = 60t + 60.
We simplify this equation and find t
90t - 60t = 60
30t = 60
t = 60/30 = 2 hours.
Now we know that the travel time for A to get the meeting point was 2 hours;
hence, the travel time for train C was 1 hour less that that, or 2-1 = 1 hour.
At this point, we can find the total distance PQ. It is the sum of partial distances
for train A and train C to get the meeting point, or
90*2 + 120*1 = 180 + 120 = 300 kilometers.
ANSWER. The distance from P to Q is 300 kilometers.
Solved.
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As you see from this solution, the basic skills required is an ability to solve
standard basic Travel @ Distance problems, and combining different aspects of them.
For simple Travel & Distance problems, see introductory lessons
- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.
They are written specially for you.
You will find the solutions of many basic problems there.
Read them and learn once and for all from these lessons on how to solve simple Travel and Distance problems.
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