Question

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

Answer 1

To find the distance traveled through the mountains, set up a proportion using the speeds and distances given. Solve the equation to find the distance.

Step-by-step explanation:

To find the distance traveled through the mountains, we first need to determine the distance traveled across the plains. Let's set up a proportion to find the time taken for each part of the trip:

x / 90 = (300 - x) / 37.5

Cross-multiplying gives us:

37.5x = 90(300 - x)

Simplifying the equation:

37.5x = 27000 - 90x

127.5x = 27000

x ≈ 211.76

Hence, approximately 211.76 miles of the trip were through the mountains.

Answer 2

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.

`(x)/(y)=90------(1)`

Also,

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

i.e.

`(300-x)/(3.8-y)=37.5------(2)`

From equation (1) we have:

`x=90y`

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

`(300-90y)/(3.8-y)=37.5`

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)