There are A point and B point and there is a moving walkway with a fixed speed between A and B.
Taro and Jiro began to walk at the same time on this moving walkway with a fixed speed respectively from A point.
While Taro walks four steps, Jiro walks three steps.
The step length of Jiro is 48 cm and it is 0.8 times of the step length of Taro.
Taro arrived at B point in 80 steps exactly.
Jiro arrived at B point later than Taro for 16 seconds.
If this moving walkway has stopped, Taro could walk by 112 steps exactly from A point to B point.
Answer each of following questions.
(1) Find the speed of the moving walkway.
(2) Find the number of steps in which Jiro walked on the moving walkway from A point to B point.
Taro and Jiro began to walk at the same time on this moving walkway with a fixed speed respectively from A point.
While Taro walks four steps, Jiro walks three steps.
The step length of Jiro is 48 cm and it is 0.8 times of the step length of Taro.
Taro arrived at B point in 80 steps exactly.
Jiro arrived at B point later than Taro for 16 seconds.
If this moving walkway has stopped, Taro could walk by 112 steps exactly from A point to B point.
Answer each of following questions.
(1) Find the speed of the moving walkway.
(2) Find the number of steps in which Jiro walked on the moving walkway from A point to B point.
Answer
Since Taro walks by 112 steps between A and B when the moving platform has stopped, the distance between A and B is 60 cm × 112= 6720 cm.
Since Jiro walks three steps while Taro walks four steps, the ratio of the distance walked in the same time is (60 cm × four steps) : (48 cm × three steps) = 5 : 3.
Thus, the ratio of speed is also Taro : Jiro = 5 : 3.
Taro takes 112 steps between A and B. If Taro rides and walk on the moving walkway, Taro reaches in 80 steps.
While Taro walks 80 steps, a moving walkway moves forward by 112 - 80 = 32 steps.
Therefore, the ratio [ of the speed of Taro and a moving walkway is 80 steps : 32 steps = 5 : 2.
The ratio of speed is made into a continued ratio, Taro : Jiro : moving walkway = 5 : 3 : 2.
Moreover, the speed of Taro + walking way is described 5 + 2 = 7 as the sum of the speed ratio.
The speed of Jiro + moving walkway is 3 + 2 = 5.
Jiro took 16 seconds more than Taro for arriving at B.
The ratio of the time is an inverse ratio of the ratio of speed and it is Taro : Jiro = 5 : 7. 7 - 5 = 2 which is a difference of this ratio is equivalent to 16 seconds which is actual time difference.
Thus, the time when Taro arrives at B from A is 16 seconds / 2 x 5 = 40 seconds.
In 40 seconds the walkway moves by 32 Taro’s steps, it moves 60 cm × 32 steps = 1920 cm in 40 seconds.
Therefore the speed of the walkway is 1920 cm / 40 seconds = 48 cm/second.
The ratio of the distance is the same as the ratio of speed 3 : 2.
The distance Jiro walked on the walkway to B from A is 6720 cm × 3/(3+2) = 4032 cm.
Since the stride of Jiro is 48 cm, the number of steps Jiro walked is 4032 cm / 48 cm = 84 steps.
(1) 48 cm / second
(2) 84 steps
(2) 84 steps
Solution
(1) The stride of Taro is 48 cm / 0.8 = 60cm.
Since Taro walks by 112 steps between A and B when the moving platform has stopped, the distance between A and B is 60 cm × 112= 6720 cm.
Since Jiro walks three steps while Taro walks four steps, the ratio of the distance walked in the same time is (60 cm × four steps) : (48 cm × three steps) = 5 : 3.
Thus, the ratio of speed is also Taro : Jiro = 5 : 3.
Taro takes 112 steps between A and B. If Taro rides and walk on the moving walkway, Taro reaches in 80 steps.
While Taro walks 80 steps, a moving walkway moves forward by 112 - 80 = 32 steps.
Therefore, the ratio [ of the speed of Taro and a moving walkway is 80 steps : 32 steps = 5 : 2.
The ratio of speed is made into a continued ratio, Taro : Jiro : moving walkway = 5 : 3 : 2.
Moreover, the speed of Taro + walking way is described 5 + 2 = 7 as the sum of the speed ratio.
The speed of Jiro + moving walkway is 3 + 2 = 5.
Jiro took 16 seconds more than Taro for arriving at B.
The ratio of the time is an inverse ratio of the ratio of speed and it is Taro : Jiro = 5 : 7. 7 - 5 = 2 which is a difference of this ratio is equivalent to 16 seconds which is actual time difference.
Thus, the time when Taro arrives at B from A is 16 seconds / 2 x 5 = 40 seconds.
In 40 seconds the walkway moves by 32 Taro’s steps, it moves 60 cm × 32 steps = 1920 cm in 40 seconds.
Therefore the speed of the walkway is 1920 cm / 40 seconds = 48 cm/second.
(2) The ratio of the speed of Jiro and a moving walkway is Jiro : moving walkway = 3 : 2.
The ratio of the distance is the same as the ratio of speed 3 : 2.
The distance Jiro walked on the walkway to B from A is 6720 cm × 3/(3+2) = 4032 cm.
Since the stride of Jiro is 48 cm, the number of steps Jiro walked is 4032 cm / 48 cm = 84 steps.
