SOLUTION: Distance between two stations X and Y is 220 km. Trains P and Q leave station X at 8 am and 9.51 am respectively at the speed of 25 km/hr and 20 km/hr respectively for journey towa

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Question 1027372: Distance between two stations X and Y is 220 km. Trains P and Q leave station X at 8 am and 9.51 am respectively at the speed of 25 km/hr and 20 km/hr respectively for journey towards Y. Train R leaves station Y at 11.30 am at a speed of 30 km/hr for journey towards X. When and where will P be at equal
distance from Q and R ?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!


The time taken by P, Q, R to reach some point enroute is the same.
They start at different times and speeds
Equate time of P & Q
Equate time of P & r
and solve the equations
P &Q
(x+d)/25 = x/20 + 1 51/60

(x+d)/25 -x/20 = 37/20
20x+20d -25x = 37*20*25/20
-5x +20d = 925
/-5
x-4d= -185.......................(1)
P& R
(x+d)/25 = (220-x-2d)/30 +7/2
(x+d)/25 -(220-x-2d)/30 =7/2
30x+30d -25*220+25x+50d = 30*25*7/2
55x+80d =8125......................(2)

V1.00 x -4.00 d = -185.00 .............1
Total value
55.00 x + 80.00 d = 8125.00 .............2
Eliminate y
multiply (1)by 20.00
Multiply (2) by 1.00
20.00 x -80.00 d = -3700.00
55.00 x + 80.00 d = 8125.00
Add the two equations
75.00 x = 4425.00
/ 75.00
x = 59.00
plug value of x in (1)
1.00 x -4.00 d = -185.00
59.00 -4.00 d = -185.00
-4.00 d = -185.00 -59.00
-4.00 d = -244.00
d = 61.00
you can calculate real time easily
m.ananth@hotmail.ca