Question

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Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes. But if he travels to 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

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Answer 1

$\underline{\sf{\blue{Question}}}$

• Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes. But if he travels to 260 km by train and 240 km by takes he takes 6 minutes longer. Find the speed of the train and that of the taxi.

$\underline{\sf{\green{Answer}}}$

• Speed of train = 100km/h
• Speed of taxi = 80km/h

${\sf{\orange{Question}}}$

• Abdul travelled 300km by train & 200km by taxi
• Time taken = 5 hours 30 minutes
• Abdul travelled 360km by train & 240km by taxi
• Time taken = 6 min longer

${\sf{\purple{To\:Calculate}}}$

Let the Speed of the train = x km/h

Speed of taxi = y km/h

$\underline{\sf{\green{According\:To\: Question}}}$

Case I

Distance covered by train = 300 km

Then

Time taken by train (t1) = 300/x

And

Distance covered by taxi = 200km

So

Time taken by taxi = (t2) = 200/y

Now

➻ t1 + t2 = 5+ (30/60)

➻ 300/x + 200/y = 5+(30/60)

➻ 300/x + 200/y = 11/2____________(1)

Case II

Distance covered by train = 260km

Then

Time taken by train (t3) = 260/x

And

Distance covered by taxi = 240km

Then

Time taken by taxi (t4) = 240/y

➻ t3 + t4 = 5+(36/60)

➻ 260/x + 240/y = 28/5____________(2)

Now

Let 1/x = a , Let 2/y = b

Then

From equation 1 and 2

➻ 300a + 200b = 11/2

➻ 100(3a + 2b) = 11/2

➻ 3a + 2b = 11/200____________(3)

And

➻ 260a + 240b = 28/5

➻ 20(13a + 12b) = 28/5

➻ 13a + 12b = 28/100____________(4)

On multiplying equation 3 by 6

➻ 6(3a + 2b = 11/200)

➻ 18a + 12b = 66/200____________(5)

On Subdtracting equation 4 from 5

18a + 12b = 66/200

13a + 12b = 28/100

- - -

______________________

5a = 66/200 - 26/100

➻ 5a = (66-56)/200

➻ 5a = 10/200

➻ a = 1/20×5

➻ a = 1/100

➻ 1/x = 1/100

➻ x = 100

From equation 3 put a = 1/100

➻ 3/100 + 2b = 11/200

➻ 2b = 11/200-3/100

➻ 2b - 5/200

➻ 2b = 1/40

➻ b = 1/80

➻ 1/y = 1/80

➻ y = 80

$\underline{\sf{\green{Hence}}}$

• Speed of train = 100km/h
• Speed of taxi = 80km/h

________________________

Hope it's helpful :)

Answer 2

$\underline{\sf{blue{Question}}}$

• Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes. But if he travels to 260 km by train and 240 km by takes he takes 6 minutes longer. Find the speed of the train and that of the taxi.

$\underline{\sf{green{Answer}}}$

• Speed of train = 100km/h
• Speed of taxi = 80km/h

${\sf{orange{Question}}}$

• Abdul travelled 300km by train & 200km by taxi
• Time taken = 5 hours 30 minutes
• Abdul travelled 360km by train & 240km by taxi
• Time taken = 6 min longer

${\sf{purple{To\:Calculate}}}$

Let the Speed of the train = x km/h

Speed of taxi = y km/h

$\underline{\sf{green{According\:To\: Question}}}$

Case I

Distance covered by train = 300 km

Then

Time taken by train (t1) = 300/x

And

Distance covered by taxi = 200km

So

Time taken by taxi = (t2) = 200/y

Now

➻ t1 + t2 = 5+ (30/60)

➻ 300/x + 200/y = 5+(30/60)

➻ 300/x + 200/y = 11/2____________( 1 )

Case II

Distance covered by train = 260km

Then

Time taken by train (t3) = 260/x

And

Distance covered by taxi = 240km

Then

Time taken by taxi (t4) = 240/y

➻ t3 + t4 = 5+(36/60)

➻ 260/x + 240/y = 28/5____________( 2 )

Now

Let 1/x = a , Let 2/y = b

Then

From equation 1 and 2

➻ 300a + 200b = 11/2

➻ 100(3a + 2b) = 11/2

➻ 3a + 2b = 11/200____________( 3 )

And

➻ 260a + 240b = 28/5

➻ 20(13a + 12b) = 28/5

➻ 13a + 12b = 28/100____________( 4 )

On multiplying equation 3 by 6

➻ 6(3a + 2b = 11/200)

➻ 18a + 12b = 66/200____________( 5 )

On Subdtracting equation 4 from 5

18a + 12b = 66/200

13a + 12b = 28/100

- - -

__________________________

5a = 66/200 - 26/100

➻ 5a = (66-56)/200

➻ 5a = 10/200

➻ a = 1/20×5

➻ a = 1/100

➻ 1/x = 1/100

➻ x = 100

From equation 3 put a = 1/100

➻ 3/100 + 2b = 11/200

➻ 2b = 11/200-3/100

➻ 2b - 5/200

➻ 2b = 1/40

➻ b = 1/80

➻ 1/y = 1/80

➻ y = 80

$\underline{\sf{purple{Hence}}}$

• Speed of train = 100km/h
• Speed of taxi = 80km/h

____________________________

Hope it's helpful :)