There is a running course of 3.2 km one round.
Taro and Jiro run to the same direction three round from the same position.
Taro began to run at 200 m/m and Jiro began to run at 240 m/m 3 minutes afterward.
When Taro finished running one round, he stopped and drank water.
While he was drinking water, he was passed by Jiro.
Then, Taro began to run at 260 m/m, he caught up with Jiro 3 minutes afterward.
Then, although Taro ran with the same speed as Jiro, when they finished running two round, Taro walked at 80 m/m.
Furthermore, after that, Taro began to run at 200 m/m and finished running three round later than Jiro for 7 minutes and 10 seconds.
Answer the following questions.
(1) Find the time while Taro was drinking water.
(2) Find the distance where two persons ran with the same speed.
(3) Find the distance where Taro walked.
Answer
(1) 35 seconds
(2) 2420 m
(3) 600 m
Solution
(1)
3200 / 200 = 16 minutes = Time for Taro to run one round
3200 + 260 × 3 = 3980 m = Distance for Taro to catch up with Jiro
3980 / 240 = 199/12 minutes = Time for Jiro to run
199/12 + 3 = 235/12 minutes = Time for Taro to run from start point
235/12 - 16 - 3 = 7/12 minutes = 35 seconds
(2)
3200 × 2 - 3980 = 2420 m
(3)
3200 / 240 = 40/3 minutes = Time for Jiro to run one round
40/3 + 7 minutes and 10 seconds = 41/2 minutes = Time for Taro to run last one round
(200 × 41/2 - 3200) / (200 - 80) = 15/2 minutes = Time for Taro to walk
80 × 15/2 = 600 m
