From home to the post office, mother and her child walked side by side together.
Mother's step was longer than child's step by 20 cm.
Mother took 200 steps and child took 300 steps from home to the post office.
Find the distance from home to the post office?
Mother's step was longer than child's step by 20 cm.
Mother took 200 steps and child took 300 steps from home to the post office.
Find the distance from home to the post office?
Answer
Since the proportion of number of steps is 200 : 300 = 2 : 3, the proportion of stride length of mother and child is 3 : 2.
The difference of stride length is 3 - 2 = 1 by the ratio.
Since 1 is equivalent to 20cm by the actual length, 3 of mother’s stride length is 20cm × 3 = 60cm.
Therefore, as for the distance from home to the post office is 40cm × 300steps ＝ 12000cm＝120m.
When the children walked 200 steps, the difference is 20cm × 200steps = 4000cm.
Since child took 300 steps from home to the post office , child takes 300 - 200 = 100steps for 4000cm.
Then, the lenght of child is found to be 4000cm/100steps ＝ 40cm.
Therefore, the distance from home to the post office is 40cm × 300 steps = 12000cm = 120m.
120 m
Solution
When they walk ahead the same distance, stride length and the number of steps become the inverse proportion.
Since the proportion of number of steps is 200 : 300 = 2 : 3, the proportion of stride length of mother and child is 3 : 2.
The difference of stride length is 3 - 2 = 1 by the ratio.
Since 1 is equivalent to 20cm by the actual length, 3 of mother’s stride length is 20cm × 3 = 60cm.
Therefore, as for the distance from home to the post office is 40cm × 300steps ＝ 12000cm＝120m.
<Another solution>
One step of mother and child makes 20cm difference.
When the children walked 200 steps, the difference is 20cm × 200steps = 4000cm.
Since child took 300 steps from home to the post office , child takes 300 - 200 = 100steps for 4000cm.
Then, the lenght of child is found to be 4000cm/100steps ＝ 40cm.
Therefore, the distance from home to the post office is 40cm × 300 steps = 12000cm = 120m.
