Question

Лео и Тиг соревнуются на в дистанции 100 км.Лео бежит со скоростью на 15 км/ч большей,чем Тиг.Начали друзья одновременно,но Лео прибыл к финишу на 6 часов раньше.С какой скоростью бежал Тиг?​

Answer 1

Ответ:

скорость Тига 10 км/ч.

Объяснение:

Пусть скорость Тига - х км/ч Тогда скорость Лео - (х+15) км/ч.

Тиг прибежал к финишу через 100/х ч. Лео прибежал к финишу через ((100/(х+15)) ч. Разница между финишированим бегунов - 6 ч:

100/x-100/(х+15)=6;

[100(х+15)-100x-6х(х+15)]/[x(x+15)]=0;

x(x+15)≠0;

100x+1500-100x-6x²-90=0

-6x²-90x+1500=0;

x≠0;

6x²+90x-1500=0; √D=√(8100+24*1500)=210

x₁₂=(-90±210)/12;

x₁=-300/12 <0 - не подходит;

x₂=120/12=10;

Ответ: скорость Тига 10 км/ч.

Скорость Лео - 25 км/ч. Хорошо бегут (по условию они именно бегут) ребята. Быстро.

Answer 2

Problem Analysis

We are given that Leo and Tig are competing in a race over a distance of 100 km. Leo runs at a speed that is 15 km/h faster than Tig. Both friends started at the same time, but Leo arrived at the finish line 6 hours earlier than Tig. We need to determine the speed at which Tig was running.

Solution

Let's assume that Tig's speed is x km/h. Since Leo runs at a speed that is 15 km/h faster than Tig, Leo's speed can be represented as x + 15 km/h.

We know that the time taken by Leo to complete the race is 6 hours less than the time taken by Tig. Let's represent the time taken by Tig as t hours. Therefore, the time taken by Leo can be represented as t - 6 hours.

We can use the formula speed = distance / time to calculate the time taken by each friend to complete the race.

For Leo: - Speed = x + 15 km/h - Distance = 100 km - Time = t - 6 hours

For Tig: - Speed = x km/h - Distance = 100 km - Time = t hours

Using the formula, we can set up the following equations:

Leo: Speed = Distance / Time x + 15 = 100 / (t - 6)

Tig: Speed = Distance / Time x = 100 / t

We can solve these equations to find the value of x, which represents Tig's speed.

Calculation

Let's solve the equations:

From the equation for Leo: x + 15 = 100 / (t - 6)

From the equation for Tig: x = 100 / t

To eliminate x, we can subtract the equation for Tig from the equation for Leo:

(x + 15) - x = (100 / (t - 6)) - (100 / t)

Simplifying the equation:

15 = (100t - 100(t - 6)) / (t(t - 6))

15 = (100t - 100t + 600) / (t(t - 6))

15 = 600 / (t(t - 6))

Cross-multiplying:

15t(t - 6) = 600

Expanding and rearranging the equation:

15t^2 - 90t - 600 = 0

Dividing the equation by 15:

t^2 - 6t - 40 = 0

Using the quadratic formula:

t = (-(-6) ± √((-6)^2 - 4(1)(-40))) / (2(1))

t = (6 ± √(36 + 160)) / 2

t = (6 ± √196) / 2

t = (6 ± 14) / 2

t = (6 + 14) / 2 or t = (6 - 14) / 2

t = 20 / 2 or t = -8 / 2

t = 10 or t = -4

Since time cannot be negative, we discard the negative value.

Therefore, Tig took 10 hours to complete the race.

To find Tig's speed, we substitute the value of t into the equation for Tig:

x = 100 / t

x = 100 / 10

x = 10 km/h

Answer

Tig ran at a speed of 10 km/h.

Verification

Let's verify the answer using the given information:

Leo's speed = Tig's speed + 15 km/h = 10 km/h + 15 km/h = 25 km/h

Leo's time = Tig's time - 6 hours = 10 hours - 6 hours = 4 hours

Distance = Speed * Time = 25 km/h * 4 hours = 100 km

The distance covered by both Leo and Tig is 100 km, which matches the given information. Therefore, the answer is verified.

Conclusion

Tig ran at a speed of 10 km/h.