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

Answer:

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.

$\dfrac{x}{y}=90------(1)$

Also,

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

i.e.

$\dfrac{300-x}{3.8-y}=37.5------(2)$

From equation (1) we have:

$x=90y$

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

$\dfrac{300-90y}{3.8-y}=37.5$

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)

Answer 2

The train travelled 3 hours across the plain and 0.8 hours across the mountains.

Speed

Speed is the ratio of the distance travelled to time taken. It is given by:

Speed = distance / time

Let d₁ represent the distance covered in the plain at time t₁ and d₂ represent the distance covered in the mountain at time t₂.

• 90 = d₁ / t₁
• d₁ = 90t₁  (1)

Also:

• 37.5 = d₂ / t₂
• d₂ = 37.5t₂  (2)

d₁ + d₂ = 300

90t₁ + 37.5t₂ = 300    (3)

t₁ + t₂ = 3 hours 48 minutes

t₁ + t₂ = 3.8   (4)

Solving equations 3 and 4 simultaneously gives:

t₁ = 3, t₂ = 0.8

The train travelled 3 hours across the plain and 0.8 hours across the mountains.

Find out more on speed at: https://brainly.com/question/4931057