Expert: Lynn Houston - 7/21/2009

Question
Hello. I was curious if you could help me with these problems. Thank you so much!




1.   An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it.  Find the speed of each train.



2.   One year ago Walt invested $12,000. He invested part of the money at 7% and the rest at 9%. He made a total of $970 in interest. How much was invested at 7%?


Answer
1. An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it.  Find the speed of each train.

distance = speed * time or d=st

Let t = the time for the local train and s = the speed for the local.  So you know for the express train, distance = 60, speed = 2s and time = t-2 (60 = 2s(t-2).  For the local, distance = 60, speed = s and t = time (60 = st), the equations are equal so

st = 2s(t-2)
st = 2st - 4s
4s = st
4 = t  (insert into one of the eqs to solve for s)

60 = s(4)
s = 15

So, the local train averages 15 mph, while the express train averages 30 mph.



2. One year ago Walt invested $12,000. He invested part of the money at 7% and the rest at 9%. He made a total of $970 in interest. How much was invested at 7%?

let x = amt invested at 9%, therefore 12,000-x = amt invested at 7%

.09x + .07(12000-x) = 970
.09x + 840 - .07x = 970
.02x = 130
x = $6500 invested at 9%, therefore, $5500 invested at 7%