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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

$\huge \underline {\sf{ \blue{Question : - }}}$

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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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$\huge \: \underline { \sf {\orange{Answer : - }}}$

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• Speed of train = 100km/h

• Speed of taxi = 80km/h

$\:$

$\huge \underline {\boxed {\bf{ \sf{Given : - }}}}$

• Abdul travelled 300km by train & 200km by taxi

• Time taken = 5 hours 30 minutes

• Abdul travelled 260km by train & 240km by taxi

• Time taken = 6 min longer

$\:$

$\huge\underline { \sf{ \purple{To \: Calculate : - }}}$

$\:$

• Speed of the train & taxi

$\:$

$\huge \underline {\sf{ \green{Explanation : - }}}$

$\:$

• Let the Speed of the train = x km/h

• Speed of taxi = y km/h

$\:$

$\underline{ \boxed{ \sf {\bf{According \: To \: Question : : }}}}$

$\:$

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 , 1/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 Subtracting 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 = 1/1000

➺ 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

$\:$

$\huge\underline { \boxed{ \sf{ \frak{ \pink{Hence}}}}}$

$\:$

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

$\:$

___________________________________________

Answer 2

$\huge \underline {\sf{ \blue{Question : - }}}$

$\:$

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 taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

$\:$

$\huge \: \underline { \sf {\orange{Answer : - }}}$

$\:$

• Speed of train = 100km/h

• Speed of taxi = 80km/h

$\:$

$\huge \underline {\boxed {\bf{ \sf{Given : - }}}}$

• Abdul travelled 300km by train & 200km by taxi

• Time taken = 5 hours 30 minutes

• Abdul travelled 260km by train & 240km by taxi

• Time taken = 6 min longer

$\:$

$\huge\underline { \sf{ \purple{To \: Calculate : - }}}$

$\:$

• Speed of the train & taxi

$\:$

$\huge \underline {\sf{ \green{Explanation : - }}}$

$\:$

• Let the Speed of the train = x km/h

• Speed of taxi = y km/h

$\:$

$\underline{ \boxed{ \sf {\bf{According \: To \: Question : : }}}}$

$\:$

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 , 1/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 Subtracting 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 = 1/1000

➺ 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

$\:$

$\huge\underline { \boxed{ \sf{ \frak{ \pink{Hence}}}}}$

$\:$

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

$\:$

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