On level ground, 24 kilometers can be traversed in 12 minutes. On the incline the speed is cute in half. How many kilometers can be transversed on the incline in 48 minutes?

Question

On level ground, 24 kilometers can be traversed in 12 minutes. On the incline the speed is cut in half. How many kilometers can be transversed on the incline in 48 minutes?

Answer 1

On flat ground, 24 kilometers can be traversed in 12 minutes, so 24km in 12min.

On the incline, the speed is cut in half, which you can think of and use in multiple ways.

One way would be to find the speed right off the bat, first without the incline.

So 24km in 12min, I will write it as 24/12 km/min to think of it and see it as one number, and the unit is kilometers per minute: km/min.

We can simplify this: 24/12 = 2, and the unit stays the same, so 2 km/min.

That is our speed on flat ground, without the incline, 2 km/min. Now lets find the speed on the incline.

"On the incline the speed is cut in half", so if you cut that in half, our speed on the incline is 1 km/min.

Knowing our speed on the incline is all we need to figure out how much distance we could go in 48 minutes.

In 48 minutes on the incline, at 1 kilometer per minute, you could traverse 48 kilometers.

Another way to solve this, without finding the exact speed to start, is to adjust the distance or the time it took on the flat ground, based on our info that the speed is cut in half on the incline.

Here's what I mean by that:

If the speed is cut in half, you could cover the same amount of distance, but it would take you twice as long.

So that 24km in 12min, would take twice as long, so 24km in 24min, since 12 minutes x 2 = 24 minutes.

So on the incline, we can cover 24km in 24mins, and we want to know how far we can go in 48 minutes.

Luckily, 24 minutes is half of 48 minutes, so if we can go 24km in 24 minutes, we can double it to find our answer. 24km x 2 = 48km.

48km in 48min on the incline.

If the speed is cut in half, you would cover half as much distance in the same amount of time,

so 12km in 12min, rather than 24km in 12min.

So we are going 12km in 12min on the incline, and we want to know how far we can go in 48 minutes.

12 minutes is one quarter of 48 minutes (48÷4=12).

Using this, we can multiply our 12-minute distance by 4 to see how far we could go in the full 48 minutes.

So if we can go 12km in 12min on the incline, and 12 minutes x 4 = 48 minutes, then:

12km x 4 = 48km.

Answer 2

The speed on level ground is 24 kilometers / 12 minutes. Do you see how speed is written here similarly, but not identically, to miles per hour?

The speed on the incline is half that, meaning it is 12 kilometers / 12 minutes. I like to set up proportions to solve these and many other types of problems. So,

12 kilometers x kilometers

------------------- = ---------------------

12 minutes 48 minutes

There are several ways to solve this. Often, we use cross-multiplication to get the equation: 12(48) = 12x. Immediately, in this case, you can see that x must be 48. So, the answer is that 48 kilometers on the incline can be transversed in 48 minutes, assuming the speed is constant.

Answer 3

the formula you use is distance = rate * time... d = rt.

what is your RATE on level ground? solve the formula for r. r = d/t.

r = 24km / 12 mins = 2 km/min.

on incline, the rate is half the level-ground rate, so it is 1 km/min.

go back to the formula to solve for the number of km (distance) you can travel in 48 minutes (time) at the speed of 1 km/min (rate). d = rt

d = (1 km/min)(48 min) = 48 km.

[notice above there is min in the bottom of the first fraction, and min in the top of the second fraction, so they cancel when multiplied. this leaves you with km, which you know is the type of answer you want.]

Answer 4

24km / 12 min = 2 km/min = speed on level ground

So, speed on the incline = 1 km / min

Distance traversed on the incline in 48 min = (1 km/min)(48 min) = 48 km