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 12

Question

pychu

3 months ago

9

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 12

0 miles per hour downhill, how long will it take to travel 45 miles per flat land?

Mathematics

2 answers:

Svet_ta [12.7K] · Answer 1 · 2026-02-26T21:47:04+03:00

The duration required for the train to cover a distance of $45{\text{ miles}}$ on flat terrain is $\boxed{30{\text{ minutes}}}.$ .

Explanation:

Speed, distance, and time are related by the formula,

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

Given:

The train's downhill speed is noted as $120{\text{ miles per hour}}$ .

A train travels downhill at double the speed it can ascend, and at 2/3 the speed uphill in comparison to flat ground.

Discussion:

Assuming the train’s downhill speed is $2x{\text{ miles/hour}}.$ , we can find its uphill speed as $x{\text{ miles/hour}}.$ and flat speed as $\dfrac{3}{2}x{\text{ miles/hour}}.$ .

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

The uphill speed is determined as follows,

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

The ground level speed comes out to be,

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

Finally, the time to cover 45 miles is deduced as follows,

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

The accommodation for the train traveling on flat terrain for a distance of $45{\text{ miles}}$ is $\boxed{30{\text{ minutes}}}.$ .

tester [12.3K] · Answer 2 · 2026-02-26T21:50:00+03:00

The train descends at twice the speed compared to its ascent, and it travels at 2/3 of the speed uphill relative to flat terrain.
If its speed downhill is measured at 120 miles per hour, its uphill speed would be 120 divided by 2, equaling 60 miles per hour, and its speed on flat ground would be 60 divided by (2/3), simplified to (60 times 3) divided by 2, resulting in 90 miles per hour.
Consequently, for the train to cover 45 miles on flat terrain, the time required is calculated as 45 divided by 90, which is equal to 0.5 hours, or 30 minutes.