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# Two men walk the same distance, one at 4 km/h and the other at 3 km/h. The first arrives 30 minutes earlier. Find the distance

by T Santhosh

**Updated **Jul 23, 2024

## Two men walk the same distance, one at 4 km/h and the other at 3 km/h. The first arrives 30 minutes earlier. Find the distance

To find the distance traveled by two men walking at different speeds where one arrives half an hour earlier than the other, follow these steps

Let the speed of the first man be 4 km/h

Let the speed of the second man be 3 km/h

Let t be the time taken by the first man to cover the distance.

The time taken by the second man is t + 0.5 hours, since he arrives half an hour later than the first man.

Since both men cover the same distance, the distance D can be expressed as

D = 4 x t

for the first man,

D = 3 x (t + 0.5)

for the second man

Setting the two distance expressions equal gives

4t = 3 x (t + 0.5)

solve for t

4t = 3t + 1.5

t = 1.5 hours

Substitute t = 1.5 hours into the distance formula for the first man

D = 4 x 1.5 = 6 km

Therefore, the distance covered by each man is 6 kilometres.

## Distance, Speed, and Time Calculations

In mathematics, problems involving distance, speed, and time are common and useful for understanding various real-world scenarios. When two individuals travel the same distance but at different speeds, the time each person takes to complete the journey can differ.

#### Understanding the Problem:

When two people travel the same distance at different speeds, the time each person takes to complete the journey will vary. If one person arrives earlier than the other, the difference in their arrival times can be used to determine the distance traveled.

#### Setting Up the Problem:

To solve this, first define the speeds of both individuals and the difference in their arrival times. For example, one person might walk at 4 km/h, while the other walks at 3 km/h. The person traveling faster will reach the destination earlier.

#### Formulating Equations:

Use the relationship between speed, time, and distance to set up equations. The basic formula is:

Distance = Speed x Time

If one person arrives 30 minutes (or 0.5 hours) earlier, you can create equations based on their speeds and the times they take to cover the same distance.

#### Solving the Equations:

Set up equations based on the distances covered by each person and solve for the unknown variables. By equating the distances traveled and solving for the time, you can find the distance.

#### Applications:

This approach is widely used in various applications, such as calculating travel times, determining speeds for transportation planning, and solving logistical problems. It helps in understanding how different factors affect travel duration and distance.