SOLUTION: A freight train made two 180 km trips. It made the second trip in 3 hours less time by increasing the rate of travel by 10km/h. Find each rate at which the train left.

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Question 628981: A freight train made two 180 km trips. It made the second trip in 3 hours less time by increasing the rate of travel by 10km/h. Find each rate at which the train left.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
1st trip:
+d+=+r%2At+
(1) +180+=+r%2At+
2nd trip:
(2) +180+=+%28+r+%2B+10+%29%2A%28+t+-+3+%29+
---------------------------
(2) +180+=+r%2At+%2B+10t+-+3r+-+30+
and
(1) +r+=+180%2Ft+
Substitute (1) into (2)
(2) +180+=+%28180%2Ft%29%2At+%2B+10t+-+3%2A%28180%2Ft%29+-+30+
(2) +180+=+180+%2B+10t+-+3%2A%28180%2Ft%29+-+30+
(2) +0+=++%2B+10t+-+3%2A%28180%2Ft%29+-+30+
(2) +30+=+10t+-+3%2A%28180%2Ft%29+
Multiply both sides by +t+
(2) +30t+=+10t%5E2+-+540+
(2) +10t%5E2+-+30t+-+540+=+0+
(2) +t%5E2+-+3t+-+54+=+0+
(2) +%28+t+-+9+%29%2A%28+t+%2B+6+%29+=+0+
Since +t+ must be positive,
+t+=+9+ is the answer
---------------------
(1) +180+=+r%2At+
(1) +180+=+r%2A9+
(1) +r+=+180%2F9+
(1) +r+=+20+
+r+%2B+10+=+30+
The rate for the 1st trip was 20 km/hr
The rate for the 2nd trip was 30 km/hr
check:
(2) +180+=+%28+r+%2B+10+%29%2A%28+t+-+3+%29+
(2) +180+=+%28+20+%2B+10+%29%2A%28+9+-+3+%29+
(2) +180+=+30%2A6+
(2) +180+=+180+
OK