Respuesta :
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.
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.
The time taken by the train to travel a distance of [tex]45{\text{ miles}}[/tex] on the flat land is [tex]\boxed{30{\text{ minutes}}}.[/tex]
Further explanation:
The relationship between speed, distance and time can be expressed as follows,
[tex]\boxed{{\text{Speed}} = \frac{{{\text{Distance}}}}{{{\text{Dime}}}}}[/tex]
Given:
The speed of the train if it goes downhill is [tex]120{\text{ miles per hour}}[/tex]
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 [tex]2x{\text{ miles/hour}}.[/tex]
So the speed of the train if it goes uphill is [tex]x{\text{ miles/hour}}.[/tex]
And the speed train on the ground level is [tex]\dfrac{3}{2}x{\text{ miles/hour}}.[/tex]
The speed of the train if it goes downhill is [tex]120{\text{ miles per hour}}[/tex]
The speed of the train if it goes uphill can be calculated as follows,
[tex]\begin{aligned}2x&= 120\\x&= \frac{{120}}{2}\\x&=60\\\end{aligned}[/tex]
The speed of the train on the ground level can be calculated as follows,
[tex]\begin{aligned}\frac{2}{3}\times {\text{Speed}}&= 60\\{\text{Speed}}&= \frac{{60 \times 3}}{2}\\&= 90{\text{ miles/hour}}\\\end{aligned}[/tex]
Therefore, the time taken to cover a distance of 45 miles can be calculated as follows,
[tex]\begin{aligned}{\text{Time}}&=\frac{{{\text{Distance}}}}{{{\text{Speed}}}}\\{\text{Time}}&= \frac{{45}}{{90}}\\&=\frac{1}{2}{\text{ hours}}\\\end{aligned}[/tex]
The time taken by the train to travel a distance of [tex]45{\text{ miles}}[/tex] on the flat land is [tex]\boxed{30{\text{ minutes}}}.[/tex]
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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.
