Question

Помогите решить задачу. Из деревни выехал велосипед, а в след за ним через 1 ч 35 мин выехал мотоциклист и догнал его через 46 мин. Сколько времени был в пути велосипедист до встречи с мотоциклистом?

Answer 1

1ч35мин*2=3ч10мин
3ч10мин+46мин=3ч56мин

Answer 2

Problem Analysis

We are given that a cyclist left the village on a bicycle, and after 1 hour and 35 minutes, a motorcyclist left and caught up with the cyclist after 46 minutes. We need to find out how much time the cyclist was on the road before meeting the motorcyclist.

Solution

To solve this problem, we can use the concept of relative speed. The relative speed between the cyclist and the motorcyclist is the sum of their individual speeds. Let's assume the speed of the cyclist is x km/h and the speed of the motorcyclist is y km/h.

We know that the motorcyclist caught up with the cyclist after 46 minutes, which is 46/60 = 23/30 hours. During this time, the motorcyclist covered the same distance as the cyclist did in 1 hour and 35 minutes, which is 1 + 35/60 = 1 + 7/12 = 19/12 hours.

Using the formula distance = speed × time, we can set up the following equation:

(x + y) × (23/30) = x × (19/12)

Simplifying the equation, we get:

(x + y) × (23/30) = x × (19/12)

Multiplying both sides by 30 and 12 to eliminate the denominators, we get:

12(x + y) × 23 = 30x × 19

Expanding and simplifying, we get:

276x + 276y = 570x

Rearranging the equation, we get:

570x - 276x = 276y

Simplifying further, we get:

294x = 276y

Dividing both sides by 276, we get:

x = (276/294)y

Now, we need to find the value of x in terms of y. To do that, we can assume a value for y and calculate the corresponding value of x.

Let's assume y = 1 km/h. Substituting this value into the equation, we get:

x = (276/294) × 1 = 0.9388

Therefore, the speed of the cyclist is approximately 0.9388 km/h when the speed of the motorcyclist is 1 km/h.

Now, we can calculate the time taken by the cyclist to meet the motorcyclist. Let's assume the time taken by the cyclist is t hours.

Using the formula distance = speed × time, we can set up the following equation:

x × t = (x + y) × (23/30)

Substituting the values of x and y into the equation, we get:

0.9388 × t = (0.9388 + 1) × (23/30)

Simplifying the equation, we get:

0.9388 × t = 1.9388 × (23/30)

Multiplying both sides by 30 to eliminate the denominator, we get:

28.164 × t = 1.9388 × 23

Dividing both sides by 28.164, we get:

t = (1.9388 × 23) / 28.164

Calculating the value, we get:

t ≈ 1.5886 hours

Therefore, the cyclist was on the road for approximately 1.5886 hours before meeting the motorcyclist.

Answer

The cyclist was on the road for approximately 1.5886 hours before meeting the motorcyclist.