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.
Answer
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.
□ : 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,
Since the ratio of the speed turns into an inverse ratio of the time ratio,
the speed ratio is Taro : Jiro = 7 : 5.
