There is a straight road connecting A point and B point.
Taro walks from A point to B point and Jiro walks from B point to A point with a fixed speed respectively.
Both of them started at the same time and passed on the way.
25 minutes after passing, Taro arrived at B point and Jiro arrived at A point the 24 minutes after Taro’s arrival.
Find the least integer ratio of the speed of Taro and Jiro.
Taro walks from A point to B point and Jiro walks from B point to A point with a fixed speed respectively.
Both of them started at the same time and passed on the way.
25 minutes after passing, Taro arrived at B point and Jiro arrived at A point the 24 minutes after Taro’s arrival.
Find the least integer ratio of the speed of Taro and Jiro.
Answer
Since Jiro took 25 + 24 = 49 minutes to walk the same distance Taro walked in □ minutes,
Since the ratio of the time to walk the same distance becomes the same, the proportional expression of A is equal to B.
□ : 49 = 25 : □.
49 × 25 = □ × □
49 × 25 = 7 × 7 × 5 × 5 = 7 × 5 × 7 × 5
Thus, □ = 7 × 5 = 35.
Therefore the ratio of time to walk the same distance is Taro : Jiro = 35 : 49 = 5 : 7.
Since the ratio of the speed turns into an inverse ratio of the time ratio,
7 : 5
Solution
The time taken from the start until passing is assumed □.
Since Jiro took 25 + 24 = 49 minutes to walk the same distance Taro walked in □ minutes,
the ratio of the time to walk the same distance is Taro : Jiro = □ : 49 -------A.
Next, Since Jiro took □ minutes to walk the same distance Taro walked in 25 minutes,
the ratio of the time to walk the same distance is Taro : Jiro = 25 : □ -------B.
Since the ratio of the time to walk the same distance becomes the same, the proportional expression of A is equal to B.
□ : 49 = 25 : □.
49 × 25 = □ × □
49 × 25 = 7 × 7 × 5 × 5 = 7 × 5 × 7 × 5
Thus, □ = 7 × 5 = 35.
Therefore the ratio of time to walk the same distance is Taro : Jiro = 35 : 49 = 5 : 7.
Since the ratio of the speed turns into an inverse ratio of the time ratio,
the speed ratio is Taro : Jiro = 7 : 5.
