Atrain 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 hours and 48 minutes, how much of it was through the mountains?

The distance traveled by train in mountains is:

                     30 miles.

Time taken by train in mountains is:

                 0.8 hours( 48 minutes)

Step-by-step explanation:

Let the distance traveled by a train in plains be: x miles.

Time taken in plains to travel x mile= y hours.

Hence, distance traveled by train in mountains is: 300-x miles.

( Since a train travels  a total of 300 miles)

Time taken in mountains is: 3.8-y hours

( Since train total takes a time of 3 hours and 48 minutes

3 hours and 48 minutes=3+48/60 hours

                                       =3+0.8 hours

                                       = 3.8 hours )

Now, average speed in plains is: 90 miles per hour.

i.e.

Also,

Average speed of train in mountains is:37.5 miles per hour

i.e.

From equation (1) we have:

on putting the value of x in equation (2) we get:

Now on solving we get:

y=3

Similarly x=270.

Hence, the distance traveled by the train in mountains is:

30 miles.

Time taken by train in mountains is: 48 minutes

( Since, 300-x=300-270=30 miles.

and 3.8-y=3.8-3=0.8 hours

which is equal to 48 minutes)

d

step-by-step explanation:

i used the pitagoras theoreme