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

speed uphill=120/2=60

speed level=3/2 * uphill=90
speed downhill=120

on flat land, d=45=90*t
t=1/2 hr

Well, if a train goes twice as fast downhill as it does uphill, I can only imagine the uphill part must be a real slow chug. And if it goes 2/3 as fast uphill as it does on level ground, then it's in for a real uphill struggle.

So, let's break it down. If the train goes 120 mph downhill, then uphill it must be going at a mere 60 mph (half of downhill speed). And since it goes 2/3 as fast uphill as it does on level ground, we can calculate that it goes at approximately 90 mph on flat land (2/3 of 120 mph).

Now, to travel 45 miles on flat land at a speed of 90 mph, we can divide the distance by the speed to find the time it takes. So, 45 miles divided by 90 mph gives us 0.5 hours, or 30 minutes.

So, it will take the train approximately 30 minutes to travel 45 miles on flat land. And during that time, it will have the perfect balance of speed and no pesky hills to slow it down. Enjoy the ride!

Let's assume the speed of the train on level ground is x mph.

Given that the train goes twice as fast downhill as it can go uphill, its speed uphill would be (1/2)*x mph.

Also, it goes 2/3 as fast uphill as it can go on level ground. So, its speed uphill can be calculated as (2/3) * x mph.

Given that the train's speed downhill is 120 mph, we can set up the equation:

120 mph = 2 * (2/3) * x mph

Now, let's solve for x:

120 mph = (4/3) * x mph

Multiply both sides by 3/4 to isolate x:

(120 mph) * (3/4) = x mph

90 mph = x mph

So, the speed of the train on level ground is 90 mph.

To find the time it takes to travel 45 miles on flat land, we can use the formula:

Time = Distance / Speed

Plugging in the values:

Time = 45 miles / 90 mph

Simplifying:

Time = 0.5 hours

Therefore, it will take 0.5 hours (or 30 minutes) to travel 45 miles on flat land.

To solve this problem, let's break it down step by step.

Step 1: Determine the speed of the train uphill.
We are given that the train goes twice as fast downhill as it goes uphill. Therefore, if the train's speed downhill is 120 mph, the speed uphill would be half of that: 120 mph ÷ 2 = 60 mph.

Step 2: Determine the speed of the train on flat ground.
We are also given that the train's speed uphill is 2/3 of its speed on level ground. So, if the speed uphill is 60 mph, we need to find the speed on level ground. Let's call it x mph. Using the given information, we can set up the following equation: 2/3 * x = 60 mph. Solving this equation, we find x = (60 mph * 3) / 2 = 90 mph. Therefore, the speed on flat ground is 90 mph.

Step 3: Calculate the time it takes to travel 45 miles on flat land.
The formula to calculate time is: Time = Distance ÷ Speed.
Given that the distance is 45 miles and the speed on flat ground is 90 mph, we can calculate the time it takes to travel: Time = 45 miles ÷ 90 mph = 0.5 hour or 30 minutes.

So, it will take 30 minutes for the train to travel 45 miles on flat land.