A cyclist travels for x hours at 5km/h he travels 35km/h altogether and his average speed is 7km/h find x and y
this is not the question i typed in
To find the values of x and y, we need to use the given information and set up a system of equations.
Let's start by defining the variables:
- x: The time (in hours) the cyclist travels at 5 km/h
- y: The time (in hours) the cyclist travels at a different speed
Now, let's use the given information to set up the equations:
1. The total distance traveled is equal to the sum of the distances traveled at each speed:
5x + y = 35 ... (equation 1)
2. The average speed is calculated by dividing the total distance traveled by the total time taken:
Average Speed = Total Distance / Total Time
Given that the average speed is 7 km/h, we have:
7 = (5x + y) / (x + y) ... (equation 2)
Now, we have a system of two equations with two variables. Let's solve it:
First, let's rewrite equation 2:
7(x + y) = 5x + y
Expanding the equation:
7x + 7y = 5x + y
Combining like terms:
7x - 5x + 7y - y = 0
Simplifying:
2x + 6y = 0 ... (equation 3)
Now, we have two equations:
5x + y = 35 ... (equation 1)
2x + 6y = 0 ... (equation 3)
We can solve this system using any method like substitution or elimination. Let's use the elimination method.
Multiplying equation 1 by 2 allows us to create opposite coefficients for x when we add the equations:
10x + 2y = 70
2x + 6y = 0
Subtracting the second equation from the first:
(10x + 2y) - (2x + 6y) = 70 - 0
8x - 4y = 70
Dividing this equation by 4 to simplify it:
2x - y = 17 ... (equation 4)
Now, we have a new equation:
2x - y = 17 ... (equation 4)
2x + 6y = 0 ... (equation 3)
Next, we can eliminate the x variable by subtracting equation 4 from equation 3:
(2x + 6y) - (2x - y) = 0 - 17
2x - 2x + 6y + y = -17
7y = -17
Dividing by 7:
y = -17 / 7
y ≈ -2.43
Now that we have the value of y, we can substitute it back into one of the previous equations to find x.
Using equation 3:
2x + 6(-2.43) = 0
Simplifying:
2x - 14.58 = 0
2x = 14.58
x = 14.58 / 2
x ≈ 7.29
Therefore, the values of x and y are approximately:
x ≈ 7.29 hours
y ≈ -2.43 hours
Note: The negative value for y indicates that the cyclist traveled backward at the given speed. If we consider only positive values of y, the solution would be x ≈ 7.29 hours and y ≈ 2.43 hours.
I can't figure what you mean by
he travels 35km/h altogether and his average speed is 7km/h