a cyclist rides for 5 hours at a certain speed and then for 4 hours at a speed 6 km/h greater than her original speed. If he rides 294 km altogether, what was her initial speed?
slower speed ---- x km/h
faster speed ----- x+6 km/h
5x + 4(x+6) = 294
easy to solve....
30
Well, to solve this problem, let's get the cyclist off their bike for a second and use a bit of math humor!
Let's call the cyclist's original speed "x" km/h. So, for the first 5 hours, the cyclist traveled a distance of 5x km.
For the next 4 hours, the cyclist increased their speed by 6 km/h more than their original speed, making it x + 6 km/h. So, during this time, the cyclist traveled a distance of 4(x + 6) km.
Now, to find the total distance traveled, we just add these two distances together:
5x + 4(x + 6) = 294
Simplifying the equation, we get:
5x + 4x + 24 = 294
Combining like terms:
9x + 24 = 294
Subtracting 24 from both sides:
9x = 270
Finally, dividing both sides by 9:
x = 30
So, the cyclist's initial speed was 30 km/h. Keep pedaling with laughter!
Let's assume the cyclist's initial speed is "x" km/h.
In the first 5 hours, the cyclist covers a distance of 5x km.
In the next 4 hours, the cyclist covers a distance of 4(x+6) km (as the speed is 6 km/h greater than the initial speed).
The total distance covered by the cyclist is 294 km, so we can set up the following equation:
5x + 4(x+6) = 294
Expanding the equation, we get:
5x + 4x + 24 = 294
Combining like terms, we have:
9x + 24 = 294
Subtracting 24 from both sides, we get:
9x = 270
Dividing both sides by 9, we have:
x = 30
Therefore, the cyclist's initial speed was 30 km/h.
To find the initial speed of the cyclist, let's break down the problem into steps:
Step 1: Assign variables and define the problem:
Let's assume the cyclist's original speed is "x" km/h. Since the cyclist rides for 5 hours at this speed, the distance covered can be calculated as 5x km.
Additionally, the cyclist rides for another 4 hours at a speed 6 km/h greater than the original speed, which means the speed for the second leg is (x + 6) km/h. So, the distance covered in the second leg is 4(x + 6) km.
Overall, the total distance covered is 294 km.
Step 2: Set up the equation:
Since the total distance covered is the sum of the distances covered in each leg, we can set up the equation as:
5x + 4(x + 6) = 294
Step 3: Solve the equation:
Now, we solve the equation:
5x + 4x + 24 = 294
Combining like terms:
9x + 24 = 294
Subtracting 24 from both sides of the equation:
9x = 270
Dividing both sides by 9:
x = 30
Step 4: Interpret the result:
The initial speed of the cyclist is 30 km/h.
Therefore, the initial speed of the cyclist was 30 km/h.