Answer the following questions.
(1) Taro continues walking first 3km at 4 km/h and afterwards at 3 km/h.
Find the distance he walks in 2 hours.
(2) 2 hours after Taro leaves, Jiro pursues Taro from the same point. Jiro moves first 4 km at 15 km/h and afterwards at 12 km/h by bicycle.
Find the time when Jiro catches up with Taro after Jiro’s leaving.
(1) Taro continues walking first 3km at 4 km/h and afterwards at 3 km/h.
Find the distance he walks in 2 hours.
(2) 2 hours after Taro leaves, Jiro pursues Taro from the same point. Jiro moves first 4 km at 15 km/h and afterwards at 12 km/h by bicycle.
Find the time when Jiro catches up with Taro after Jiro’s leaving.
Answer
As he moves at 3km/h in the remaining time, total distance in 2 hours is 3km + 3km/h × (2 - 3/4) = 3 + 3.75 = 6.75km.
(2) The time Jiro moves 4 km at 15 km/h is 4 km / 15 km/h = 4/15 hours.
The distance between Taro and Jiro when Jiro moved 4km is 6.75km + 3 km/h × 4/15 hour - 4km = 3.55km.
Jiro pursues Taro for this distance at 12 km/h.
The time for Jiro to catch up with Taro is 3.55 km / (12 - 3) km/h = 71/180 hours.
Therefore the time when Jiro catches up with Taro after Jiro’s leaving is (4/15 + 71/180) × 60 = 119/3 minutes.
(1) 6.75 km
(2) 119/3 minutes
(2) 119/3 minutes
Solution
(1) When Taro moves 3 km at 4 km/h, it takes 3 km/4 km/hr = 3/4 hours.
As he moves at 3km/h in the remaining time, total distance in 2 hours is 3km + 3km/h × (2 - 3/4) = 3 + 3.75 = 6.75km.
(2) The time Jiro moves 4 km at 15 km/h is 4 km / 15 km/h = 4/15 hours.
The distance between Taro and Jiro when Jiro moved 4km is 6.75km + 3 km/h × 4/15 hour - 4km = 3.55km.
Jiro pursues Taro for this distance at 12 km/h.
The time for Jiro to catch up with Taro is 3.55 km / (12 - 3) km/h = 71/180 hours.
Therefore the time when Jiro catches up with Taro after Jiro’s leaving is (4/15 + 71/180) × 60 = 119/3 minutes.
