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A train travels at a constant rate. If t...

A train travels at a constant rate. If the train takes 13 minutes to travel m kilometers, how long will the train take to travel n kilometers?

A

`(13m)/(n)`

B

`(13n)/(m)`

C

`13mn`

D

`(m)/(13)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we can follow these instructions: ### Step 1: Understand the Given Information We know that a train travels at a constant rate. It takes 13 minutes to travel a distance of \( m \) kilometers. ### Step 2: Determine the Time Taken to Travel 1 Kilometer To find out how long it takes the train to travel 1 kilometer, we can divide the total time taken by the distance traveled: \[ \text{Time to travel 1 km} = \frac{13 \text{ minutes}}{m \text{ km}} = \frac{13}{m} \text{ minutes/km} \] ### Step 3: Calculate the Time Taken to Travel \( n \) Kilometers Now, to find out how long it will take to travel \( n \) kilometers, we can multiply the time taken to travel 1 kilometer by \( n \): \[ \text{Time to travel } n \text{ km} = n \times \left(\frac{13}{m}\right) = \frac{13n}{m} \text{ minutes} \] ### Final Answer Thus, the train will take \(\frac{13n}{m}\) minutes to travel \( n \) kilometers. ---
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