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?

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) (Show Source): You can put this solution on YOUR website!
Let = time spent on highway in hours
= time spent on back road in hours
Let = distance traveled on highway in miles
= distance traveled on back roads in miles
--------------------------------------------------
On highway:
(1)
On back roads:
(2)
--------------------------
(2)
Substitute (1) into (2)
(2)
(2)
(2)

------------------
You spent 4 hrs on highway
You spent 2 hrs on back roads
---------------------------
check:
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK

Answer by ankor@dixie-net.com(22740) (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
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