Question

A person goes on foot from village A to village B at a speed of 4 km/hour. If he walks at a speed of 5km/hour, he reaches village B, 7 minutes earlier. Find the distance between the villages.
$step \: by \: step \: solution$
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Answer 1

Step-by-step explanation:

difference in time = 7min = 7/60 hr

let distance be 'x'.

distance/speed = time

x/4 - x/5 = 7/60

x = 140/60 = 2 1/3 km

distance between the villages

= 2 1/3 km Answer

Answer 2

The distance between the villages is $2\dfrac{1}{3}\ km$ .

Explanation:

Let d be the distance between two villages.

Given : A person goes on foot from village A to village B at a speed of 4 km/hour.

Since $\text{Time}=\dfrac{\text{Distance}}{\text{Speed}}$

Time to walk from village A to village B  $t_1=\dfrac{d}{4}$ hours

If he walks at a speed of 5 km/hour, he reaches village B, 7 minutes earlier.

Time to walk from village A to village B  $t_2=\dfrac{d}{5}$ hours

Since 7 minutes = $\dfrac{7}{60}$ hour . [∵ 1 hour = 60 minutes and 1 minute = $\dfrac{1}{60}$ hour]

According to question :

$t_1-\dfrac{7}{60}=t_2\\\\\Rightarrow\ \dfrac{d}{4}-\dfrac{d}{5}=\dfrac{7}{60}\\\\\Rightarrow\ \dfrac{5d-4d}{20}=\dfrac{7}{60}\\\\\Rightarrow\ \dfrac{d}{20}=\dfrac{7}{60}\\\\\Rightarrow\ d=\dfrac{7}{3}$

$\Rightarrow\ d=2\dfrac{1}{3}\ km$

Hence, the distance between the villages is $2\dfrac{1}{3}\ km$ .

# Learn more :

A bicyclist was traveling from the village to the railroad station with a speed of 15 mph and he was coming back to the village with a speed of 10 mph. Find the distance from the village to the railroad station, if it’s known that it took 1 more hour for the bicyclist to get back to the village.

https://brainly.com/question/9007640