SOLUTION: The speed of train A is 8mph slower than the speed of train B. Train A travels 230 miles in the same time it takes train B to travel 270 miles. Find the speed of both trains. T

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The speed of train A is 8mph slower than the speed of train B. Train A travels 230 miles in the same time it takes train B to travel 270 miles. Find the speed of both trains. T      Log On


   

Question 328438: The speed of train A is 8mph slower than the speed of train B. Train A travels 230 miles in the same time it takes train B to travel 270 miles. Find the speed of both trains.
Thank you
Found 2 solutions by checkley77, josmiceli:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT
TRAIN A: 230=(R-8)T
T=230/(5-8)
TRAIN B: 270=RT
T=270/R
230/(R-8)=270/R CROSS MULTIPLY.
270(R-8)=230R
270R-2,160=230R
270R-230R=2,160
40R=2,160
R=2,160/40
54 MPH FOR TRAIN B.
PROOF:
230/(54-8)=270/54
230/46=270/54
5=5

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need 2 equations:
d%5BA%5D+=+r%5BA%5D%2At%7BA%5D
230+=+%28r%5BB%5D+-+8%29%2At%5BA%5D
and
d%5BB%5D+=+r%5BB%5D%2At%5BB%5D
270+=+r%5BB%5D%2At%5BB%5D
You are given that t%5BA%5D+=+t%5BB%5D, so
230%2F%28r%5BB%5D+-+8%29+=+270%2Fr%5BB%5D
Multiply both sides by r%5BB%5D%2A%28r%5BB%5D+-+8%29
230r%5BB%5D+=+270%2A%28r%5BB%5D+-+8%29
230r%5BB%5D+=+270r%5BB%5D+-+2160
40r%5BB%5D+=+2160
r%5BB%5D+=+54
and, since
r%5BA%5D+=+r%5BB%5D+-+8
r%5BA%5D+=+54+-+8
r%5BA%5D+=+46
The speed of train A is 46 mi/hr
The speed of train B is 54 mi/hr
check answers:
d%5BA%5D+=+r%5BA%5D%2At%5BA%5D
230+=+46%2At%5BA%5D
t%5BA%5D+=+230%2F46
t%5BA%5D+=+5 hrs
and
d%5BB%5D+=+r%5BB%5D%2At%5BB%5D
270+=+54%2At%5BB%5D
t%5BB%5D+=+270%2F54
t%5BB%5D+=+5 hrs
t%5BA%5D+=+t%5BB%5D
OK