2 cyclists start from the same point and ride in opposite directions. 1 rides twice as fast as the other. In 3 hours they are 90km apart. What is the rate of each cyclist? I figured out the answer is 20km/h and 10km/h. What I don't know and need help with is how to write the equations? If anyone could help me with this it would be much appreciated. Thank You
a = 2 b
3(a + b) = 90
Thank Scott but I did figure out the answer I just don't know how to write the equation for it, can you show me the equation? Thank You again
speed of slower rider --- x km/h
speed of faster rider ---- 2x km/h
distance gone by slower = 3(x) = 3x
distance gone by faster = 3(2x) = 6x
3x + 6x = 90
9x = 90
x = 10
rate of slower rider = 10 km/h
rate of faster rider = 2(10) = 20 km/h
To solve this problem, we can set up two equations for the two cyclists.
Let's say the slower cyclist's rate is x km/h. Since the faster cyclist rides twice as fast, their rate would be 2x km/h.
The distance traveled by each cyclist is rate multiplied by time. So, in 3 hours, the slower cyclist would have traveled a distance of 3x km, and the faster cyclist would have traveled a distance of 3(2x) = 6x km.
Since they are riding in opposite directions, their distances add up to the total distance of 90 km:
3x + 6x = 90
Simplifying the equation:
9x = 90
Dividing both sides of the equation by 9:
x = 10
Therefore, the slower cyclist's rate is 10 km/h, and the faster cyclist's rate is twice that, which is 20 km/h.