SOLUTION: Steve made a business trip of 318 miles. He averaged 54 mph for the first part of the trip and 61 mph for the second part. If the trip took 5.5 hours, how long did he travel at e

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Steve made a business trip of 318 miles. He averaged 54 mph for the first part of the trip and 61 mph for the second part. If the trip took 5.5 hours, how long did he travel at e      Log On

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Question 1033338: Steve made a business trip of 318 miles. He averaged 54 mph for the first part of the trip and 61 mph for the second part. If the trip took 5.5 hours, how long did he travel at each rate?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in miles
traveled on 1st part of trip
Let +t+ = time in hrs for 1st
part of trip
--------------------------
1st part of trip:
(1) +d+=+54t+
2nd part of trip:
(2) +318+-+d+=+61%2A%28+5.5+-+t+%29+
----------------------------
(2) +318+-+d+=+335.5+-+61t+
(2) +d+=+61t+-+17.5+
Substitute (1) into (2)
(2) +54t+=+61t+-+17.5+
(2) +7t+=+17.5+
(2) +t+=+2.5+
and
+5.5+-+t+=+5.5+-+2.5+
+5.5+-+t+=+3+
--------------------
He traveled for 2.5 hrs at 54 mi/hr
He traveled for 3 hrs at 61 mi/hr
------------------------------
check:
(1) +d+=+54t+
(1) +d+=+54%2A2.5+
(1) +d+=+135+ mi
and
(2) +318+-+d+=+61%2A%28+5.5+-+t+%29+
(2) +318+-+d+=+61%2A%28+5.5+-+2.5+%29+
(2) +318+-+d+=+61%2A3+
(2) +318+-+d+=+183+
(2) +d+=+318+-+183+
(2) +d+=+135+ mi
OK