Question

A cowboy takes his herd from A to C via B. if he goes from A to B at 4km/h and from B to C at 6 km/h, the trip will take 5 hours and 25 minutes. If he travels the first stretch at 6km/h and the second at 4km/h, it will take 5 hours.

Given the travel speed of a cowboy from point A to B and B to C, find the distances between A and B and between B and C if the travel times are specified.

Answer 1

The distance between A and B is approximately 15.03 km and the distance between B and C is approximately 9.98 km.

Step-by-step explanation:

To find the distances between A and B and between B and C, we can use the equation:

Distance = Speed x Time

Let's denote the distance between A and B as x and the distance between B and C as y.

From the given information, we can set up the following equations:

x/4 + y/6 = 5 hours and 25 minutes = 5.42 hours

x/6 + y/4 = 5 hours

Multiplying both sides of the first equation by 12, we get:

3x + 2y = 65.04

Multiplying both sides of the second equation by 12, we get:

2x + 3y = 60

Multiplying the first equation by 2 and the second equation by 3 to eliminate x, we get:

6x + 4y = 130.08

6x + 9y = 180

Subtracting the second equation from the first equation, we get:

5y = 49.92

y = 9.98

Substituting y back into the second equation, we get:

2x + 3(9.98) = 60

2x + 29.94 = 60

2x = 60 - 29.94

2x = 30.06

x = 15.03

Therefore, the distance between A and B is approximately 15.03 km and the distance between B and C is approximately 9.98 km.