Question

Решите двумя арифметическими способами следующую задачу: Мотоциклист, двигаясь со скоростью 40 км/ч, проехал некоторое расстояние за 12 минут.. За сколько минут проедет это расстояние велосипедист, двигаясь со скоростью 15 км/ч?

Answer 1

12 минут = 12:60 = 0,2 часа 
Мотоциклист проехал 40*0,2 = 8 км.
Велосипедист проедет за 8:15 = 8/15 часа или 32 минуты.

Скорость велосипедиста в 15/40 = 3/8 раза меньше, значит, времени затратит в 8/3 больше.
12*8/3 = 32 минуты.

Answer 2

Problem Analysis

We are given that a motorcyclist travels a certain distance at a speed of 40 km/h in 12 minutes. We need to find out how long it will take a cyclist, traveling at a speed of 15 km/h, to cover the same distance.

Solution 1: Using the formula Distance = Speed × Time

We can use the formula Distance = Speed × Time to solve this problem. Let's denote the distance covered by the motorcyclist as D1 and the time taken by the cyclist as T2.

For the motorcyclist: - Speed = 40 km/h - Time = 12 minutes = 12/60 hours (since 1 hour = 60 minutes)

Using the formula Distance = Speed × Time, we can calculate the distance covered by the motorcyclist: D1 = 40 km/h × (12/60) hours

Now, we need to find the time taken by the cyclist to cover the same distance. Let's denote this time as T2.

For the cyclist: - Speed = 15 km/h - Distance = D1 (the same distance covered by the motorcyclist)

Using the formula Distance = Speed × Time, we can calculate the time taken by the cyclist: T2 = D1 / 15 km/h

Let's calculate the values of D1 and T2 using the given information.

Solution 2: Using the ratio of speeds

Another way to solve this problem is by using the ratio of speeds. The ratio of speeds between the motorcyclist and the cyclist is 40 km/h : 15 km/h.

Since the distance covered is the same, the ratio of times taken will be the inverse of the ratio of speeds.

Let's denote the time taken by the cyclist as T2.

For the motorcyclist: - Speed = 40 km/h - Time = 12 minutes = 12/60 hours (since 1 hour = 60 minutes)

For the cyclist: - Speed = 15 km/h - Time = T2 (the time taken by the cyclist)

Using the ratio of speeds, we can set up the following equation: 40 km/h : 15 km/h = (12/60) hours : T2

Simplifying the equation, we get: 40/15 = (12/60) / T2

Let's solve this equation to find the value of T2.

Calculation

Let's calculate the values of D1 and T2 using both methods.

Solution 1: Using the formula Distance = Speed × Time - Distance covered by the motorcyclist (D1) = 40 km/h × (12/60) hours = 8 km - Time taken by the cyclist (T2) = 8 km / 15 km/h = 0.5333 hours = 0.5333 × 60 minutes ≈ 32 minutes

Solution 2: Using the ratio of speeds - T2 = (12/60) hours × (15 km/h / 40 km/h) = (12/60) hours × (3/8) = 0.3 hours = 0.3 × 60 minutes = 18 minutes

Answer

Therefore, the cyclist will take approximately 32 minutes (Solution 1) or 18 minutes (Solution 2) to cover the same distance.