<PRE><B>Question 1069142</B>
A train averages a speed of 90 miles per hour across the plains and 37.5 miles per hour through the mountains.
 If a trip of 300 miles took 3 hour and 48 minutes, how much of it was through the mountains?
:
Let d = distance traveled at 37.5 (thru the mountains)
then
(300-d) = distance traveled at 90 mph
:
Write a time equation, time = dist/speed
change 3 hr 48 min to hrs: 3 + 48/60 = 3.8 hrs
plain time + mountain time = 3.8 hrs
{{{(300-d)/90}}} + {{{d/37.5}}} = 3.8
Multiply 90*37.5
3375*{{{(300-d)/90}}} + 3375*{{{d/37.5}}} = 3.8(3375)
cancel the denominator
37.5(300-d) + 90d = 12825
11250 - 37.5d + 90d = 12825
52.5d = 1575
d = 1575/52.5
d = 30 mi thru the mountains
:
;
:
Check this, find the distance on the plain
300-30 = 270 mi
Find the actual time at each speed
270/90 = 3 hrs
30/37.5 = .8 hrs
-----------------
total time: 3.8 hrs



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