In a race, average speed of total 75 bikes is 35km/hr.The average speed of red bikes is 55 km/hr. If average speed of green bikes is 30km/hr, then how many green bikes are there?
Question
In a race, average speed of total 75 bikes is 35km/hr.The average speed of red bikes is 55 km/hr. If average speed of green bikes is 30km/hr, then how many green bikes are there?
Solution
To solve this problem, we need to use the concept of weighted averages. Here are the steps:
Step 1: Let's denote the number of red bikes as R and the number of green bikes as G. We know that R + G = 75 (total number of bikes).
Step 2: We also know that the total distance covered by all bikes is the sum of the distances covered by the red and green bikes. This can be expressed as (R55 + G30) / 75 = 35.
Step 3: Now we have a system of two equations, and we can solve it. Let's express R from the first equation: R = 75 - G.
Step 4: Substitute R in the second equation: (75 - G)55 + G30 = 75*35.
Step 5: Simplify this equation and solve it for G. You will get G = 50.
So, there are 50 green bikes in the race.
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