SOLUTION: Manuel traveled 3 hours nonstop to Mexico, a total of 167 miles. He took a train part of the way, which averaged 60mph, and then took a bus the remaining distance, whic

Algebra ->  Equations -> SOLUTION: Manuel traveled 3 hours nonstop to Mexico, a total of 167 miles. He took a train part of the way, which averaged 60mph, and then took a bus the remaining distance, whic      Log On


   

Question 1067639: Manuel traveled
3
hours nonstop to Mexico, a total of
167
miles. He took a train part of the way, which averaged
60mph,
and then took a bus the remaining distance, which averaged
50mph.
How long was Manuel on the train?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs spent on the train
+3+-+t+ = time in hrs spent on the bus
Let +d+ = distance in miles traveled by train
+167+-+d+ = distance in miles traveled by bus
---------------------------------------------
For the trip by train:
(1) +d+=+60t+
For the trip by bus:
(2) +167+-+d+=+50%2A%28+3+-+t+%29+
-----------------------------
Substitute (1) into (2)
(2) +167+-+60t+=+150+-+50t+
(2) +10t+=+17+
(2) +t+=+1.7+
and
+3+-+t+=+3+-+.7+
+3+-+t+=+2.3+
-----------------------
He was on the train for 1.7 hrs
Also note: +.7%2A60+=+42+ min
He was on the train for 1 hr 42 min
--------------------------------
check:
(1) +d+=+60t+
(1) +d+=+60%2A1.7+
(1) +d+=+102+ miles
and
(2) +167+-+d+=+50%2A%28+3+-+t+%29+
(2) +167+-+d+=+50%2A%28+3+-+1.7+%29+
(2) +167+-+d+=+50%2A1.3+
(2) +167+-+d+=+65+
and
+102+%2B+65+=+167+ miles total