SOLUTION: I need help solving this word problem. You drove 370 miles in 6 hours. You drove 70 mph on the highway and 45 mph on the back roads. How many hours did you spend on each?

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Question 944976: I need help solving this word problem. You drove 370 miles in 6 hours. You drove 70 mph on the highway and 45 mph on the back roads. How many hours did you spend on each?
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time spent on highway in hours
+6+-+t+ = time spent on back road in hours
Let +d+ = distance traveled on highway in miles
+370+-+d+ = distance traveled on back roads in miles
--------------------------------------------------
On highway:
(1) +d+=+70t+
On back roads:
(2) +370+-+d+=+45%2A%28++6+-+t+%29+
--------------------------
(2) +370+-+d+=+270+-+45t+
Substitute (1) into (2)
(2) +370+-+70t+=+270+-+45t+
(2) +100+=+25t+
(2) +t+=+4+
+6+-+t+=+6+-+4+
+6+-+t+=+2+
------------------
You spent 4 hrs on highway
You spent 2 hrs on back roads
---------------------------
check:
(1) +d+=+70t+
(1) +d+=+70%2A4+
(1) +d+=+280+
and
(2) +370+-+d+=+45%2A%28++6+-+t+%29+
(2) +370+-+d+=+45%2A2+
(2) +d+=+370+-+90+
(2) +d+=+280+
OK


Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You drove 370 miles in 6 hours.
You drove 70 mph on the highway and 45 mph on the back roads.
How many hours did you spend on each?
:
let t = time traveling at 70 mph
the total time of the trip is 6 hrs,therfore:
(6-t) = time at 45 mph
:
Write a distance equation; dist = speed * time
:
70 mph dist + 45 mph dist = 370
70t + 45(6-t) = 370
70t + 270 - 45t = 370
70t - 45t = 370 - 270
25t = 100
t = 100/25
t = 4 hrs at 70 mph
then
6 - 4 = 2 hrs at 45 mph
:
:
Confirm this, find the actual dist at each speed
70*4 = 280 mi
45*2 = 90 mi
---------------
total dist: 270 mi