The distance between A point and B point is 10 km.
Taro walks from A point at 4 km/h to B point.
He walks for 30 minutes and take a rest for 5 minutes and he repeat this time cycle.
Jiro goes to A point from B point at 12 km/h by a bicycle without taking a rest and return to B point.
Taro and Jiro left at the same time.
Find the time (time after they left) for Jiro to pass Taro.
Moreover, find the distance from A point to the point Jiro passed.
Answer
70 minutes
4 km
Solution
The time concerning Jiro reaching A point is 60 × 10/12 = 50 minutes.
He will turn up at A point and pursues Taro.
Taro walks 4 × 30/60 = 2 km in 30 minutes and he walks another 4 × 30/60 = 2 km until 65 minutes after 35 minutes.
He takes the 2nd rest at the point 4 km from A and he walks again after 70 minutes.
By the way, as for Jiro, he is in the point of 4 km from A in 70 minutes (12 × (70 - 50)/60 = 4) that means he catches up with Taro exactly 70 minutes after leaving.
Taro walks from A point at 4 km/h to B point.
He walks for 30 minutes and take a rest for 5 minutes and he repeat this time cycle.
Jiro goes to A point from B point at 12 km/h by a bicycle without taking a rest and return to B point.
Taro and Jiro left at the same time.
Find the time (time after they left) for Jiro to pass Taro.
Moreover, find the distance from A point to the point Jiro passed.
Answer
70 minutes
4 km
Solution
The time concerning Jiro reaching A point is 60 × 10/12 = 50 minutes.
He will turn up at A point and pursues Taro.
Taro walks 4 × 30/60 = 2 km in 30 minutes and he walks another 4 × 30/60 = 2 km until 65 minutes after 35 minutes.
He takes the 2nd rest at the point 4 km from A and he walks again after 70 minutes.
By the way, as for Jiro, he is in the point of 4 km from A in 70 minutes (12 × (70 - 50)/60 = 4) that means he catches up with Taro exactly 70 minutes after leaving.
