The speed of two motor cyclist A and B are in the ratio 11:12 respectively. The motorcyclist travels 4.5 km less than the motorcyclist B in the same duration What was the distance travelled by motorcyclist B?
Question
The speed of two motor cyclist A and B are in the ratio 11:12 respectively. The motorcyclist travels 4.5 km less than the motorcyclist B in the same duration What was the distance travelled by motorcyclist B?
Solution
Let's assume that the speed of motorcyclist A is 11x km/h and the speed of motorcyclist B is 12x km/h, where x is a constant.
Now, let's consider the time taken by both motorcyclists to travel the same distance. Since the time is the same for both, we can equate the distances traveled by motorcyclist A and motorcyclist B.
The distance traveled by motorcyclist A can be calculated using the formula: distance = speed × time. So, the distance traveled by motorcyclist A is 11x × t, where t is the time taken.
Similarly, the distance traveled by motorcyclist B is 12x × t.
According to the given information, motorcyclist A travels 4.5 km less than motorcyclist B in the same duration. So, we can set up the equation:
11x × t = 12x × t - 4.5
Simplifying the equation, we get:
11x × t - 12x × t = -4.5
-x × t = -4.5
Dividing both sides of the equation by -x, we get:
t = 4.5 / x
Now, we need to find the distance traveled by motorcyclist B. Substituting the value of t in the equation for the distance traveled by motorcyclist B, we get:
distance traveled by motorcyclist B = 12x × t = 12x × (4.5 / x) = 54 km
Therefore, the distance traveled by motorcyclist B is 54 km.
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