SOLUTION: A train travelled from Town A to Town B at a uniform speed. If the speed had been increased by 18m.p.h, the time taken for the journey would have been 3 hours less. If the speed ha

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Question 761352: A train travelled from Town A to Town B at a uniform speed. If the speed had been increased by 18m.p.h, the time taken for the journey would have been 3 hours less. If the speed had been reduced by 9m.p.h, the time taken for the jounry would have been 3 hours more. Find the speed of the train and the distance between Town A and Town B.
PLEASE HELP ME!!!!
thanks
Found 2 solutions by pbdesai, ptaylor:
Answer by pbdesai(4) (Show Source):
You can put this solution on YOUR website!
Speed of the train - 36/mph
Distance between A and B- 324 miles
Solution -1) b/a= c
2) b/(a+18) = (c-3)
3) b/(a-9) = (c+3)
Use this and u will solve the sum.

Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate (speed) of the train
And let d=distance between the two towns
And t=time required for the initial trip
(r+18=speed increased by 18mph)
(r-9=speed reduced by 9mph)
Now we know the following:
d=rt----------------------------eq1
d=(r+18)(t-3)-------------------eq2
d=(r-9)(t+3)--------------------eq3
Looking at eq2 and 3, we see that:
(r+18)(t-3)=(r-9)(t+3) expand each side using FOIL
rt-3r+18t-54=rt+3r-9t-27 collect like terms
-6r+27t=27----------------------eq1b
Looking at eq1 and 2, we see that:
rt=(r+18)(t-3)
rt=rt-3r+18t-54 collect like terms
-3r+18t=54----eq2b
multiply eq2b by 2 and subtract eq1b from it and we get:
(-6r+36t=108)
-(-6r+27t=27)
9t=81
t=9 hrs---- time needed for the initial trip
substitute t=9 into eq2b and we get
-3r+18*9=54
-3r=-108
r=36 mph-----initial speed of the trail
substitute r=36 mph and t=9 hr into eq1 and we get:
d=324 mi distance between the two towns
CK
324=(36+18)(9-3)
324=324
and
324=(36-9)(9+3)
324=324
OK
Hope this helps---ptaylor