Question

Велосипедист проделал путь длиной 27 км. сначала он ехал по шоссе, потом по грунтовой дороге. скорость велосипедиста по шоссе была 18 км/ч, по грунтовой дороге - 15 км/ч. известно, что по грунтовой дороге он ехал на 1,25 ч дольше, чем по шоссе. вычисли, сколько времени велосипедист ехал по шоссе и сколько- по грунтовой дороге.

Answer 1

15 км от шосе до дороги дома

Answer 2

Problem Analysis

We are given that a cyclist traveled a distance of 27 km. The cyclist first traveled on a highway at a speed of 18 km/h and then on a dirt road at a speed of 15 km/h. It is also known that the cyclist spent 1.25 hours longer on the dirt road than on the highway. We need to calculate the time the cyclist spent on the highway and the time spent on the dirt road.

Calculation

Let's assume that the time spent on the highway is t hours. Since the distance traveled on the highway is the product of the speed and time, we have:

Distance on highway = Speed on highway × Time on highway

Substituting the given values, we get:

18t = Distance on highway

Similarly, the time spent on the dirt road is t + 1.25 hours. Using the same logic, we have:

Distance on dirt road = Speed on dirt road × Time on dirt road

Substituting the given values, we get:

15(t + 1.25) = Distance on dirt road

We know that the total distance traveled is 27 km. Therefore, we can write the equation:

Distance on highway + Distance on dirt road = Total distance

Substituting the values, we get:

18t + 15(t + 1.25) = 27

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

Solution

Let's solve the equation:

18t + 15(t + 1.25) = 27

Expanding and simplifying the equation:

18t + 15t + 18.75 = 27

33t + 18.75 = 27

33t = 27 - 18.75

33t = 8.25

t = 8.25 / 33

t = 0.25

Therefore, the cyclist spent 0.25 hours (or 15 minutes) on the highway and 1.5 hours (or 90 minutes) on the dirt road.

Answer

The cyclist traveled on the highway for 0.25 hours (or 15 minutes) and on the dirt road for 1.5 hours (or 90 minutes).