SOLUTION: 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

Question 1069142: 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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
+ = 3.8
Multiply 90*37.5
3375* + 3375* = 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

RELATED QUESTIONS
A train averages a speed of 90 miles per hour across the plains and 37.5 miles per hour... (answered by josgarithmetic)

A train averages a speed of 90 miles per hour across the plains and 37.5 miles per hour... (answered by fractalier)

A train travels 315 miles across the plains in the same time it travels 175 miles in the... (answered by ptaylor)

A train travels through the mountains at an average speed of 35 miles per hour. It then... (answered by mananth)

An express train travels 193 miles between two cities. During the first 99 miles of a... (answered by richwmiller)

if you drive 45 miles per hour for 90 miles the 50 miles per hour for 50 miles and 72... (answered by Alan3354)

a train travels 102 miles with a constant speed of 36 miles per hour and another 92 Mi... (answered by Alan3354)

a train has traveled 275 miles in 5 hours . what is the speed of the train in miles per... (answered by Cromlix)

a motorcyclist travels 90 miles at rate of 20 miles per hour, if he returns same distance (answered by mananth)