Taro moves on foot and Jiro by bicycle on the road from A point to B point where is 16 km away from A point.
The speed Taro walks is 80 m per minute and the speed of the bicycle of Jiro is 200 m per minute.
Jiro left 30 minutes later after Taro.
Jiro passed Taro on the way and he rested for a while after he moved.
When 10 minutes passed since he began to rest, he met Taro, so he began to move by the same speed again immediately.
Taro did not take a rest and Jiro took a rest once to arrive at B point.
(1) How many hours and minutes later did Taro arrive at B point after Jiro arrived?
(2) How many km from A point did Jiro catch up with Taro?
(3) How many minutes and seconds did Jiro moved until the time when he took a rest after passing Taro?
Answer
(1) 1 hour 20 minutes
(2) 4 km
(3) 6 minutes 40 seconds
Solution
(1) Taro took 16000 / 80 = 200 minutes from A to B. Jiro took 16000 / 200 + 10 = 90 minutes.
Since Jiro left 30 minutes after Taro, time to be found is 200 - 90 - 30 = 80 minutes = 1 hour 20 minutes.
(2) 30 minutes after Taro's departure, Taro is 80 × 30 = 2400 m from A.
The time for Jiro to catch up with Taro is 2400 / (200 - 80) = 20 minutes.
The distance from A = 200 × 20 = 4000 m = 4 km.
(3) 80 × 10 = 800 m is the distance between Taro and Jiro when Jiro started to take a rest.
Jiro took 800 / (200 - 80) = 20/3 minutes = 6 minutes and 40 seconds to take a rest after passing Taro.
