Question

A bus takes 48 minutes to cover a certain distance when travelling at a speed of 50km/h. How much time will it take to cover the same distance when travelling at speed of 30km/h?

Answer 1

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✦ Required Answer:

♦️ GiveN:

• Firstly, the bus was travelling at a speed 50 km/h
• It travels for 48 minutes.

♦️ To FinD:

• Time taken to cover same distance at a speed of 30 km/h

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✦ How to Solve ?

In the first case, with speed 50 km/h and time 48 minutes, we can find the distance by using formula.

$\large{ \boxed{ \rm{ \pink{speed = \frac{distance}{time} }}}}$

Now, after getting the distance, we have to find the time taken with 2nd speed i.e. 30 km/h by using the same formula / speed, distance and time relation.

So, Let's find the solution of the problem....

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✦ Solution:

Firstly, let's do some unit conversion because speed in km/hr whereas time is in minutes. So, converting time in minutes to time in hour.

We know,

$\large{ \rm{ \longrightarrow \:60 \: minutes = 1 \: hour}} \\ \\ \large{ \rm{ \longrightarrow \: 1 \: minute = \frac{1}{60} hour}} \\ \\ \large{ \rm{ \longrightarrow \: 48 \: minutes = \cancel{\frac{48}{60} }hour = \frac{4}{5} \: hour }}$

We can rewrite the formula as,

$\large{ \rm{ \ast{ \green{ \: distance = speed \times time}}}}$

By using formula,

$\large{ \rm{ \longrightarrow \: distance = 50 \: km {h}^{ - 1} \times \frac{4}{5} hr}} \\ \\ \large{ \rm{ \longrightarrow \: distance = { \boxed{ \rm{40 \: km}}}}}$

Now, as we got the distance = 40 km and the 2nd speed of the body = 30 km/hr, we can find the time.

We can rewrite the formula as,

$\large{ \rm{ \ast{ \green{time = \dfrac{distance}{speed} }}}}$

By using formula,

$\large{ \rm{ \longrightarrow \: time = \frac{40 \: km}{30 \: km {h}^{ - 1} } }} \\ \\ \large{ \rm{ \longrightarrow \: time = \frac{4}{3} hr = \boxed{ \red{ \rm{1. \overline{33 }\: hr}}}}} \\ \\ \large{ \therefore{ \underline{ \underline{ \rm{ \purple{Hence, \: solved \: \dag}}}}}}$

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Answer 2

$\purple{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}$

$\rm{A \ bus \ takes \ 48 \ minutes \ to \ cover \ a \ certain}$

$\rm{distance \ when \ traveling \ at \ a \ speed \ of }$

$\rm{50 \ km \ hr^-1 . \ How \ much \ time \ will \ it \ take}$

$\rm{to \ cover \ the \ same \ distance \ when \ traveling}$

$\rm{at \ speed \ of \ 30 \ km \ hr^-1 \ ?}$

_________________________________________

$\purple{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}$

$\bf{\green{\therefore{\orange{Time \ taken \ by \ the \ bus \ to \ cover \ the }}}}$

$\bf{\green{\orange{same \ distance }}}$

$\bf{\green{\boxed{\orange{ = \ \frac{4}{3} hr \ = \ 1.33 \ hr }}}}$

_________________________________________

$\sf\large\underline\pink{Given:}$

$\rm{Initially,}$

$\rm{ Time \ taken \ by \ a \ bus \ to \ cover \ certain }$

$\rm{distance}$

$\rm\implies{T \ = \ 48 \ min}$

$\rm\implies{Speed \ of \ the \ bus : \ (S) \ 50 \ km \ hr^-1}$

_________________________________________

$\sf\large\underline\blue{To \ Find}$

$\rm{Time \ taken \ by \ the \ bus \ to \ cover \ the \ same }$

$\rm{distance \ at \ speed \ of \ 30 \ km \ hr^-1}$

_________________________________________

$\green{\underline{\red{\boxed{\boxed{\purple{\star{\sf Solution:}}}}}}}$

$\rm{ initially \ the \ speed \ of \ the \ bus \ is : \ 50 \ kmhr^-1}$

$\rm{and}$

$\rm{ Time \ taken \ by \ a \ bus \ to \ cover \ certain }$

$\rm{distance : \ T \ = \ 48 \ min}$

$\rm{We \ know ,}$

$\rm{\implies{60 \: minutes \ = \ 1 \: hour}}$

$\rm{\implies{ 1 \: minute = \frac{1}{60} hour}}$

$\rm{\implies{ 48 \: minutes \ = \ \cancel{\frac{48}{60} }hour = \frac{4}{5} \: hour }}$

$\rm{also,}$

$\rm{\therefore{\green{\boxed{\purple{ distance = speed \times time}}}}}$

$\rm{\implies{ distance = 50 \: km {h}^{ - 1} \times \frac{4}{5} hr}}$

$\rm{\therefore{\orange{\boxed{distance \ = \ 40 \ km}}}}$

$\rm{we \ are \ also \ given \ that }$

$\rm{the \ speed \ of \ bus \ changes \ to \ 30 \ km \ hr^-1}$

$\rm{\therefore{\green{\boxed{\purple{time = \frac{distance}{speed} }}}}}$

$\rm{\implies{ Time \ = \ \frac{40 \: km}{30 \: km {hr}^{ - 1} } }}$

$\rm\implies{Time \ = \ \frac{4 \ km}{3 \ km {hr}{-1}} \ = \ 1.33 }$

$\bf{\green{\therefore{\orange{Time \ taken \ by \ the \ bus \ to \ cover \ the }}}}$

$\bf{\green{\orange{same \ distance }}}$

$\bf{\green{\boxed{\orange{ = \ \frac{4}{3} hr \ = \ 1.33 \ hr }}}}$

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$\rm\red{Hope \ it \ helps \ :))}$