SOLUTION: TWO AUTOMOBILES TRAVEL AT THE RATE OF 50 MPH AND 30 MPH RESPECTIVELY. THE FASTER TRAVELS 2 HRS MORE THAN THE OTHER AND GOES 140 MILES FARTHER. FIND THE DISTANCE TRAVELED BY EACH.

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: TWO AUTOMOBILES TRAVEL AT THE RATE OF 50 MPH AND 30 MPH RESPECTIVELY. THE FASTER TRAVELS 2 HRS MORE THAN THE OTHER AND GOES 140 MILES FARTHER. FIND THE DISTANCE TRAVELED BY EACH.      Log On

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Question 987120: TWO AUTOMOBILES TRAVEL AT THE RATE OF 50 MPH AND 30 MPH RESPECTIVELY. THE FASTER TRAVELS 2 HRS MORE THAN THE OTHER AND GOES 140 MILES FARTHER. FIND THE DISTANCE TRAVELED BY EACH.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The faster car's time is:
+t+%2B+2+ hrs
The slower car's time is:
+t+ hrs
-----------------------
The faster car's distance is:
+d+%2B+140+
The slower car's distance is:
+d+
-------------------------
Faster car's equation:
(1) +d+%2B+140+=+50%2A%28+t+%2B+2+%29+
Slower car's equation:
(2) +d+=+30t+
--------------------
Substitute (2) into (1)
(1) +30t+%2B+140+=+50%2A%28+t+%2B+2+%29+
(1) +30t+%2B+140+=+50t+%2B+100+
(1) +20t+=+40+
(1) +t+=+2+
---------------
(2) +d+=+30t+
(2) +d+=+30%2A2+
(2) +d+=+60+ mi
and
(1) +d+%2B+140+=+50%2A%28+t+%2B+2+%29+
(1) +d+%2B+140+=+50%2A%28+2+%2B+2+%29+
(1) +d+%2B+140+=+200+
-----------------------
The faster car travels +200+ mi
The slower car travels +60+ mi