Question

A train goes twice as fast downhill as it can go uphill, and 2/3 feet as fast uphill as it can go on level ground. if it goes 120 miles per hour downhill, how long will it take to travel 45 miles per flat land?

Answer 1

Given that the train goes twice as fast downhill as it can go uphill, and 2/3 feet as fast uphill as it can go on level ground.

If it goes 120 miles per hour downhill, then its speed uphill is 120 / 2 = 60 miles per hour and its speed on a flat land is 60 / (2/3) = (60 x 3) / 2 = 180 / 2 = 90 miles per hour.

Therefore, the amount of time it will take the train to travel 45 miles on flat land is given by 45 / 90 = 0.5 hours = 30 minutes.

Answer 2

The time taken by the train to travel a distance of $45{\text{ miles}}$ on the flat land is $\boxed{30{\text{ minutes}}}.$

Further explanation:

The relationship between speed, distance and time can be expressed as follows,

$\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Dime}}}}}$

Given:

The speed of the train if it goes downhill is $120{\text{ miles per hour}}$

A train goes twice as fast downhill as it can go uphill, and 2/3 feet as fast uphill as it can go on level ground.

Explanation:

Consider the speed of the train if it goes downhill is $2x{\text{ miles/hour}}.$

So the speed of the train if it goes uphill is $x{\text{ miles/hour}}.$

And the speed train on the ground level is $\dfrac{3}{2}x{\text{ miles/hour}}.$

The speed of the train if it goes downhill is $120{\text{ miles per hour}}$

The speed of the train if it goes uphill can be calculated as follows,

$\begin{aligned}2x&= 120\\x&= \frac{{120}}{2}\\x&=60\\\end{aligned}$

The speed of the train on the ground level can be calculated as follows,

$\begin{aligned}\frac{2}{3}\times {\text{Speed}}&= 60\\{\text{Speed}}&= \frac{{60 \times 3}}{2}\\&= 90{\text{ miles/hour}}\\\end{aligned}$

Therefore, the time taken to cover a distance of 45 miles can be calculated as follows,

$\begin{aligned}{\text{Time}}&=\frac{{{\text{Distance}}}}{{{\text{Speed}}}}\\{\text{Time}}&= \frac{{45}}{{90}}\\&=\frac{1}{2}{\text{ hours}}\\\end{aligned}$

The time taken by the train to travel a distance of $45{\text{ miles}}$ on the flat land is $\boxed{30{\text{ minutes}}}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Speed and Distance

Keywords: Train, twice, fast, downhill, uphill, can go, 2/3 feet, level ground, speed, time, distance, 120 miles per hour downhill, flat land, travel, 45 miles.