Question

Велосипедист ехал 2 часа по лесной дороге и 1 час по шоссе. Всего он проехал 40 км. скорость его по шоссе была на 4км/ч больше чем скорость на лесной дороге. С какой скоростью велосипедист ехал по лесной и с какой по шоссе? Если можно то в систему уравнений

Answer 1

2х+(х+4)=40 3х=36 х=12 велосипедист ехал по лесной дороге 12км/ч 12+4=16(км/ч) по шоссе

Answer 2

Problem Analysis

We are given that a cyclist rode for 2 hours on a forest road and 1 hour on a highway, covering a total distance of 40 km. The speed on the highway was 4 km/h faster than the speed on the forest road. We need to find the speeds of the cyclist on both the forest road and the highway.

Solution

Let's assume the speed of the cyclist on the forest road is x km/h. Since the speed on the highway is 4 km/h faster, the speed on the highway is x + 4 km/h.

We can use the formula distance = speed × time to create two equations based on the given information.

Equation 1: Distance on the forest road = Speed on the forest road × Time on the forest road Equation 2: Distance on the highway = Speed on the highway × Time on the highway

We know that the total distance covered is 40 km, so we can write another equation:

Equation 3: Distance on the forest road + Distance on the highway = Total distance

Let's solve these equations to find the speeds on the forest road and the highway.

Solution Steps

1. Substitute the values into the equations: - Equation 1: 2x (distance on the forest road) = x (speed on the forest road) × 2 (time on the forest road) - Equation 2: 1(x + 4) (distance on the highway) = (x + 4) (speed on the highway) × 1 (time on the highway) - Equation 3: 2x + 1(x + 4) (distance on the forest road + distance on the highway) = 40 (total distance)

2. Simplify and solve the equations: - Equation 1: 2x = 2x - Equation 2: x + 4 = x + 4 - Equation 3: 2x + x + 4 = 40 - Simplifying Equation 3: 3x + 4 = 40 - Subtract 4 from both sides: 3x = 36 - Divide both sides by 3: x = 12

Answer

The cyclist's speed on the forest road was 12 km/h and the speed on the highway was 16 km/h.

Explanation

The cyclist rode for 2 hours on the forest road, covering a distance of 2 × 12 = 24 km. The cyclist then rode for 1 hour on the highway, covering a distance of 1 × 16 = 16 km. The total distance covered is 24 + 16 = 40 km, as given in the problem.

Therefore, the cyclist's speed on the forest road was 12 km/h and the speed on the highway was 16 km/h.