Question

Roshan travels 45km in 54 minutes. How many minutes will he take to travel 70km?

Answer 1

Hint: In this question, we are given time taken by Roshan to travel a distance of 45km and we have to calculate time taken by Roshan to travel a distance of 70km. As we know, more the distance traveled, more time will be occupied, hence the given problem is a problem of direct proportion. So we will use the formula of direct proportion to evaluate our required answer.

Complete step by step answer:
We are given that Roshan travels 45km in 54 minutes and we have to calculate time taken by Roshan to travel 70km.
As we know, more distance traveled by Roshan then more will be the time taken. Hence, the problem is of direct proportion. Let us suppose time taken by Roshan to travel 70km be y minutes.
So our table look likes:

Distance travelled	45	70
Time taken	54	y

Now, distance and time are in direct proportion. Therefore,
\[\dfrac{45}{54}=\dfrac{70}{y}\]
Cross multiplying we get:
\[45y=70\times 54\]
Dividing both sides by 45 we get:
\[\begin{align}
  & y=\dfrac{70\times 54}{45} \\
 & y=84 \\
\end{align}\]
Therefore, Rohan travels 70km in 84 minutes.
Changing minutes of hours using 1 hour = 60 minutes, we get:
$\Rightarrow 84-60=24$.
Therefore, 1 hour 24 minutes = 84 minutes.
Hence, Rohan travels 70 km in 1 hour 24 minutes.

Note: Students should note that units of both distances should be the same and since units of time are given in minutes so the answer will also be in minutes. For solving these problems, they should analyze the problem carefully and determine if it is a direct proportion or inverse proportion problem. Try to make a table to avoid confusion. Students can also solve this problem using unitary method, given as:
Time taken to travel 45km = 54 minutes.
Time taken to travel 1km = $\dfrac{54}{45}$ minutes.
Time taken to travel 70km = $\dfrac{54}{45}\times 70$ = 84 minutes.