A motorcyclist goes from Nagpur to Pune, a distance of 216 kms at an average of 36 kmph speed. Another man starts from Nagpur by car 3 hours after the first, and reaches Pune 1 hour earlier. What is the ratio of the speed of the motorcycle and the car?
Question
A motorcyclist goes from Nagpur to Pune, a distance of 216 kms at an average of 36 kmph speed. Another man starts from Nagpur by car 3 hours after the first, and reaches Pune 1 hour earlier. What is the ratio of the speed of the motorcycle and the car?
Solution
Let's solve this problem step by step:
Step 1: Calculate the time taken by the motorcyclist. We know that distance = speed × time. Given that the distance is 216 km and the average speed is 36 kmph, we can calculate the time taken by the motorcyclist using the formula: time = distance / speed. So, the time taken by the motorcyclist is 216 km / 36 kmph = 6 hours.
Step 2: Calculate the time taken by the car. We are given that the car starts 3 hours after the motorcyclist and reaches Pune 1 hour earlier. This means the car takes 6 - 1 = 5 hours to reach Pune. Since the car starts 3 hours after the motorcyclist, the total time taken by the car is 5 + 3 = 8 hours.
Step 3: Calculate the ratio of the speed of the motorcycle and the car. The ratio of the speed of the motorcycle and the car can be calculated using the formula: ratio = speed of motorcycle / speed of car. To find the ratio, we need to know the speed of the car. Let's calculate it. The speed of the car can be calculated using the formula: speed = distance / time. Given that the distance is 216 km and the time taken by the car is 8 hours, we can calculate the speed of the car as 216 km / 8 hours = 27 kmph.
Now, we can calculate the ratio of the speed of the motorcycle and the car: ratio = speed of motorcycle / speed of car = 36 kmph / 27 kmph = 4/3.
Therefore, the ratio of the speed of the motorcycle and the car is 4/3.
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