Question

The maximum speed of a train is 90 km/h. It takes 10 hours to cover a distance of 500 km. Find the ratio of its average speed to maximum speed?​

Answer 1

Answer:

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Answer 2

Answer:

5 : 9

Explanation:

As per the provided information in the given question, we have :

• Maximum speed of the train = 90 km/h
• It takes 10 hours to cover a distance of 500 km.

We've been asked to calculate the ratio of its average speed to maximum speed.

In order to calculate the ratio of its average speed to maximum speed, firstly we need to calculate the average speed.

$\odot$ Average speed of a body refers to the total distance covered by the body divided by the total time taken. Here, we are provided with the total distance travelled that is 500 km and total time taken is 10 hrs. Thus,

$\longrightarrow \sf{\quad { Speed_{(avg)} = \dfrac{Total \; Distance}{Total \; Time} }}$

Substitute the values in the formula.

$\longrightarrow \sf{\quad { Speed_{(avg)} = \cancel{\dfrac{500 \; km}{10 \; h}} }}$

$\longrightarrow \quad \underline{\boxed{ \textsf{\textbf{ Speed}}_{\textsf{\textbf{(avg)}}} = \textsf{\textbf{50 \; km}} \: \textsf{\textbf{h}}^{\textsf{\textbf{-1}}} }}$

Now, we have :

○ Maximum speed = 90 km/h

○ Average Speed = 50 km/h

$\longrightarrow \sf{\quad { Ratio = Speed_{(Avg)} \ratio Speed_{(Max)}}}$

Let's denote required ratio by R.

$\longrightarrow \sf{\quad { R = 50 \;kmh^{-1} \ratio 90 \;kmh^{-1} }}$

$\longrightarrow \sf{\quad { R =\cancel{ \dfrac{50 \;kmh^{-1}}{90 \;kmh^{-1}} }}}$

$\longrightarrow \sf{\quad { R = \dfrac{5}{9} }}$

$\longrightarrow \quad \underline{\boxed{ \textsf{\textbf{ R = 5 : 9 }} }}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

⠀⠀⠀⠀⠀★ Ratio = 5 : 9