SOLUTION: Two trains move between two towns. It takes the first train 2 hr 48 min and it takes the second 4 hr 40 min. The rate of the first train is 26 mph more than that of the second trai

Algebra ->  Expressions-with-variables -> SOLUTION: Two trains move between two towns. It takes the first train 2 hr 48 min and it takes the second 4 hr 40 min. The rate of the first train is 26 mph more than that of the second trai      Log On


   

Question 1023678: Two trains move between two towns. It takes the first train 2 hr 48 min and it takes the second 4 hr 40 min. The rate of the first train is 26 mph more than that of the second train. What is the distance between these towns?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Convert all minutes to hours:
+48%2F60+=+4%2F5+
+4%2F5+=+.8+
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+40%2F60+=+.667+
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Let +d+ = the distance between the towns
Let +s+ = the speed of the slower train in mi/hr
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Equation for the faster train:
(1) +d+=+%28+s+%2B+26+%29%2A2.8+
Equation for the slower train:
(2) +d+=+s%2A4.667+
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By substitution:
+%28+s+%2B+26+%29%2A2.8+=+s%2A4.667+
+2.8s+%2B+72.8+=+4.667s+
+1.867s+=+72.8+
+s+=+39+ mi/hr
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(1) +d+=+%28+s+%2B+26+%29%2A2.8+
(1) +d+=+%28+39+%2B+26+%29%2A2.8+
(1) +d+=+182+ mi
The distance between the towns is 182 mi
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check:
(2) +d+=+s%2A4.667+
(2) +d+=+39%2A4.667+
(2) +d+=+182+ mi
OK