SOLUTION: It is 440km to Detroit. It took me 5hours to drive there. Part of the time I was traveling 100km/h on the 401 and part of the time I was travelling 60km/h on HWY7. How long was I o

Algebra ->  Linear-equations -> SOLUTION: It is 440km to Detroit. It took me 5hours to drive there. Part of the time I was traveling 100km/h on the 401 and part of the time I was travelling 60km/h on HWY7. How long was I o      Log On


   

Question 1087615: It is 440km to Detroit. It took me 5hours to drive there. Part of the time I was traveling 100km/h on the 401 and part of the time I was travelling 60km/h on HWY7. How long was I on each road. Create and solve a system for full marks.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in km travelled on 401
+440+-+d+ = distance in km travelled on HWY7
Let +t+ = time in hrs spent on 401
+5+-+t+ = time in hrs spent on HWY7
---------------------------------------------
Equation for travelling on 401:
(1) +d+=+100t+
Equation for travelling on HWY7:
(2) +440+-+d+=+60%2A%28+5+-+t+%29+
----------------------------------
Plug (1) into (2)
(2) +440+-+100t+=+60%2A%28+5+-+t+%29+
(2) +440+-+100t+=+300+-+60t+
(2) +40t+=+140+
(2) +t+=+3.5+
and
+5+-+t+=+5+-+3.5+
+5+-+t+=+1.5+
------------------------
3.5 hrs were spent on 401
1.5 hrs were spent on HWY7
-----------------------------
check:
(1) +d+=+100t+
(1) +d+=+100%2A3.5+
(1) +d+=+350+ km
and
(2) +440+-+d+=+60%2A%28+5+-+t+%29+
(2) +440+-+d+=+60%2A%28+5+-+3.5+%29+
(2) +440+-+d+=+60%2A1.5+
(2) +440+-+d+=+90+
(2) +d+=+350+ km
OK