A cyclist and a jogger start from a town at the same time and headed for a destination 24 mi away. The rate of the cyclist is twice the rate of the jogger. The cyclist arrives 3hrs ahead of the jogger. Whats the rate of the cyclist?
C = 2J (rates)
Distance = rate/time
Therefore, time = rate/distance
J/24 - C/24 = 3
Use substitution to solve first for cyclist and then for jogger.
is the answer 12
Sorry, I goofed!
Distance = rate * time
Therefore, Time = Distance/rate
24/J - 24/C = 3
Substitute 2j for C.
24/j - 24/2J = 3
Multiply both sides by J.
24 - 12 = 3J
12 = 3j
4 = J
C = 2J = 2 * 4 = 8
Sorry for the goof! This should help.
To find the rate of the cyclist, we can use the concept of relative speed. Let's assume the rate of the jogger is 'x' miles per hour.
Since the rate of the cyclist is twice the rate of the jogger, the rate of the cyclist would be 2x miles per hour.
Let's first find out how long it takes for the cyclist to complete the 24-mile journey. We'll use the formula: time = distance / rate.
For the cyclist, time = 24 miles / (2x miles per hour) = 12/x hours.
Next, let's calculate the time it takes for the jogger to complete the same 24-mile journey. Given that the jogger arrives 3 hours later than the cyclist, we can write the equation: time of jogger = time of cyclist + 3.
Substituting the values, we get: time of jogger = 12/x + 3 hours.
Since we know that the total time for the jogger to complete the journey is 12/x + 3 hours, we can set up another equation:
12/x + 3 = 24/x
Now, we can solve this equation to find the value of x, which is the rate of the jogger.
Multiply both sides of the equation by x to eliminate fractions: 12 + 3x = 24.
Subtract 12 from both sides of the equation: 3x = 12.
Divide both sides by 3 to solve for x: x = 4.
So, the rate of the jogger is 4 miles per hour.
Finally, to find the rate of the cyclist, we multiply the rate of the jogger by 2: 4 x 2 = 8.
Therefore, the rate of the cyclist is 8 miles per hour.