Question

Велосипедист предполагал проехать дистанцию в 120 км, некоторой скоростью. Но он ехал со скоростью на 6 км/ч меньшей и поэтому прибыл в пункт значения на 1 ч позже, чем предпологал. С какой скоростью ехал велосипедист .

Answer 1

Формула пути: S=vt (S - путь, v - скорость, t- время)
составим пропорцию

S=vt=(v-6)(t+1)=120

S=vt => t=S/v=120/v

(v-6)(120/v+1)=120
120+v-720/v-6-120=0
v-720/v-6=0    \\ *v

v²-6v-720=0
D=36+2880=54²

v1=(6-54)/2=-24 (скорость не может быть отрицательной - поэтому это не наш ответ)
v2=(6+54)/2=30

Проверка:
120=30t => t=4
120=(30-6)(4+1)=24*5=120

Ответ: 30 Км/ч

Answer 2

Calculation of the Cyclist's Speed

To determine the speed at which the cyclist was traveling, we can use the information provided.

The cyclist intended to cover a distance of 120 km at a certain speed. However, they ended up traveling at a speed 6 km/h slower than planned and arrived at their destination 1 hour later than expected.

Let's denote the cyclist's intended speed as x km/h.

According to the given information, the cyclist traveled at a speed 6 km/h slower than intended, so their actual speed was (x - 6) km/h.

The time it took the cyclist to cover the distance can be calculated using the formula:

Time = Distance / Speed

The distance covered by the cyclist is 120 km, and the time taken is 1 hour longer than expected.

Substituting the values into the formula, we have:

120 km / (x - 6) km/h = (120 km / x km/h) + 1 hour

To solve this equation, we can cross-multiply and simplify:

120(x) = 120(x - 6) + x(x - 6)

Simplifying further:

120x = 120x - 720 + x^2 - 6x

Combining like terms:

0 = x^2 - 6x - 720

Now, we can solve this quadratic equation to find the value of x.