Question

Two buses do a journey between two cities 200 km apart one bus A moves at 50 kph one way and 40 kph on the return the other bus B does 45 kph on both journey

THEN FIND
(i) which bus takes less time to cover the to and fro distance

(ii) do they both take equal time ​

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Two buses A & B take a journey of 200 km

✭ Bus A travels with a speed of 50 km/h one way and 40 km/h while coming back

✭ Bus B takes 45 km/h on both the journeys

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

◈ Which bus takes less time to cover the to & fro distance?

◈ Do they both take the same time?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here we may primarily use the formula,

$\displaystyle\underline{\boxed{\sf Speed = \dfrac{Distance}{Time}}}$

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

Bus A

While it was going it would take a time of,

• Speed = 50 km/h
• Distance = 200 km

Substituting the values,

›› $\displaystyle\sf Speed = \dfrac{Distance}{Time}$

›› $\displaystyle\sf 50 = \dfrac{200}{Time}$

›› $\displaystyle\sf Time = \dfrac{200}{50}$

›› $\displaystyle\sf \green{Time_1 = 4 \ hours}$

While returning back,

• Speed = 40 km/h
• Distance = 200 km

Substituting the values,

›› $\displaystyle\sf Speed = \dfrac{Distance}{Time}$

›› $\displaystyle\sf 40 = \dfrac{200}{Time}$

›› $\displaystyle\sf Time = \dfrac{200}{40}$

›› $\displaystyle\sf \green{Time_2 = 5 \ hours}$

So then the Total time will be,

➝ $\displaystyle\sf Total \ time = T_1+T_2$

➝ $\displaystyle\sf Total \ time = 4+5$

➝ $\displaystyle\sf \orange{Total \ Time_1 = 9 \ hours}$

Bus B

This bus travels with the same speed on both the journeys,

• Speed = 45 km/h
• Distance = 200 km

Substituting the given values,

»» $\displaystyle\sf Speed = \dfrac{Distance}{Time}$

»» $\displaystyle\sf 45 = \dfrac{200}{Time}$

»» $\displaystyle\sf Time = \dfrac{200}{45}$

»» $\displaystyle\sf \purple{Time = 4.5 \ hours}$

So as it goes on two journeys the total time will be,

➳ $\displaystyle\sf Total \ time = 4.5+4.5$

➳ $\displaystyle\sf \pink{Total \ time_2 = 9 \ hours}$

$\displaystyle\therefore\:\underline{\sf Both \ the \ bus \ takes \ the \ same \ time\{9hours\}}$

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Answer 2

Answer:

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