One skier covered the distance of 20 km 20 minutes faster than the other skier. Find the speed of both skiers if one of them is travelling 2 km/hour faster than the other one.

speed of slower --- x km/h

speed of faster ---- x+2 km/h

20/x - 20/(x+2) = 20/60 = 1/3
times 3x(x+2) , the LCD

60(x+2) - 60x = x(x+2)
x^2 + 2x - 120 = 0
(x+12)(x-10) = 0
x = 10 or x = -12, the ladder is silly

The slower one went 10 km/h, and the faster went 12 km/h

check:
20/10 - 20/12
= 1/3 hr or 20 minutes.
My answer is correct

Let's say the speed of the slower skier is x km/hour.

According to the problem, the speed of the faster skier is (x + 2) km/hour.

Distance = Speed x Time

For the slower skier:
Distance = 20 km
Time = t (in hours)

For the faster skier:
Distance = 20 km
Time = t - 20/60 = t - 1/3 (converted 20 minutes to hours)

Now we can calculate the time for each skier:

Time for the slower skier = Distance/Speed = 20/x
Time for the faster skier = Distance/Speed = 20/(x + 2)

Since the faster skier is 20 minutes (1/3 hours) faster than the slower skier, we can set up the equation:

20/x = 20/(x + 2) + 1/3

To get rid of the fraction, let's multiply both sides of the equation by 3x(x + 2):

3(20)(x + 2) = 20(3x) + x(x + 2)

Now, solve for x:

60(x + 2) = 60x + x^2 + 2x

60x + 120 = 60x + x^2 + 2x

Rearranging the equation:

x^2 + 2x - 120 = 0

Now, let's solve this quadratic equation by factoring or using the quadratic formula:

(x - 10)(x + 12) = 0

Setting each factor equal to zero to solve for x:

x - 10 = 0 or x + 12 = 0

x = 10 or x = -12

Since speed cannot be negative, we disregard x = -12.

Therefore, the speed of the slower skier is 10 km/hour, and the speed of the faster skier is (10 + 2) = 12 km/hour.

To find the speeds of both skiers, we can set up a system of equations based on the given information.

Let's call the speed of the slower skier "x" km/hour. Then, the speed of the faster skier would be "x + 2" km/hour.

We know that the skier who traveled 20 km faster also took 20 minutes less time. To convert this time difference to hours, we divide by 60:

20 minutes = 20/60 = 1/3 hours

Now, using the formula Time = Distance / Speed, we can write the following equation for the slower skier:

(20 km) / x = (20 km) / (x + 2) + 1/3

To solve this equation, we can first eliminate the denominators by multiplying both sides by x(x + 2):

20(x + 2) = 20x + x(x + 2)/3

Now, distribute and simplify:

20x + 40 = 20x + (x^2 + 2x)/3

Next, multiply through by 3 to clear the fractions:

60x + 120 = 60x + x^2 + 2x

Combine like terms and rearrange the equation:

0 = x^2 + 2x - 120

Now, we can factor the quadratic equation:

0 = (x + 12)(x - 10)

Setting each factor to zero, we get:

x + 12 = 0 --> x = -12 (extraneous solution, as speed cannot be negative)
x - 10 = 0 --> x = 10

Therefore, the speed of the slower skier is 10 km/hour, and the speed of the faster skier is 10 + 2 = 12 km/hour.

So, the speeds of the skiers are 10 km/hour and 12 km/hour, respectively.