A motorcycle and a car departed from A point simultaneously toward 105 km away B point.
There is a the traffic jam section (section which it is crowded and cannot be run fast) on the way.
It took two hours for a car and one hour for a motorcycle to pass through the section.
The motorcycle arrived at B point 45 minutes earlier than the car.
Except the traffic jam section, a car advances at 75 km/h and a motorcycle advances at 60 km/h.
They progress with fixed speed respectively also in the traffic jam section.
Find the distance of the traffic jam section.
There is a the traffic jam section (section which it is crowded and cannot be run fast) on the way.
It took two hours for a car and one hour for a motorcycle to pass through the section.
The motorcycle arrived at B point 45 minutes earlier than the car.
Except the traffic jam section, a car advances at 75 km/h and a motorcycle advances at 60 km/h.
They progress with fixed speed respectively also in the traffic jam section.
Find the distance of the traffic jam section.
Answer
30 km
Solution
There is no mention where the traffic jam section is between A and B.
There is no problem even if it is considered that the traffic jam section is in the beginning and the rest is not the traffic jam section which is shown in a line segment figure.
According to this figure, although the motorcycle was 1 hour earlier than the car in the traffic jam section, it has arrived at B point early for 45 minutes.
It will be said that the time when car moved except the traffic jam section was 15 minutes shorter than motorcycle.
Since car’s speed is 75 km/h and motorcycle’s is 60 km/h except the traffic jam section, the speed ratio is 75 : 60 = 5 : 4.
The ratio of the time taken is an inverse ratio of the speed ratio and it is 4 : 5.
5 - 4 = 1 which is a difference of the time ratio is equivalent to 15 minutes which are a difference of actual time.
Since the car moved this section in time of 4, actual time is 15 minute × 4 = 60 minutes = 1 hour.
Therefore, the distance of this section is 75 km/h × 1 hour = 75 km.
The distance of the traffic jam section is 105 - 75 = 30 km.
30 km
Solution
There is no mention where the traffic jam section is between A and B.
There is no problem even if it is considered that the traffic jam section is in the beginning and the rest is not the traffic jam section which is shown in a line segment figure.
According to this figure, although the motorcycle was 1 hour earlier than the car in the traffic jam section, it has arrived at B point early for 45 minutes.
It will be said that the time when car moved except the traffic jam section was 15 minutes shorter than motorcycle.
Since car’s speed is 75 km/h and motorcycle’s is 60 km/h except the traffic jam section, the speed ratio is 75 : 60 = 5 : 4.
The ratio of the time taken is an inverse ratio of the speed ratio and it is 4 : 5.
5 - 4 = 1 which is a difference of the time ratio is equivalent to 15 minutes which are a difference of actual time.
Since the car moved this section in time of 4, actual time is 15 minute × 4 = 60 minutes = 1 hour.
Therefore, the distance of this section is 75 km/h × 1 hour = 75 km.
The distance of the traffic jam section is 105 - 75 = 30 km.
