Question

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

Answer 1

Given :-

▪ Abdul travelled distance d₁ = 300 km by train and d₂ = 200 km by taxi taking time t₁ = 5 hours 30 minutes.

▪ But, If he travels d₃ = 260 km by train and d₄ = 240 km by taxi, he takes 6 minutes longer.

To Find :-

▪ Speed of the train and that of the taxi.

Solution :-

Let the speed of the train and the bus be x km/min and y km/min respectively.

Case 1 :

☞ Distance travelled by train, d₁ = 300 km

☞ Distance travelled by taxi, d₂ = 200 km

☞ Time taken, t₁ = 5.5 hours [ 1 hr = 60 min ]

We know,

⇒ Time = Distance / Speed

Total time is given as 5.5 hours.

⇒ 300/x + 200/y = 330 [ 1 hr = 60 min ]

Let 1/x = a and 1/y = b, we get

⇒ 300a + 200b = 330

⇒ 30a + 20b = 33 ...(1)

Case 2 :

☞ Distance travelled by train, d₃ = 260 km

☞ Distance travelled by taxi, d₄ = 240 km

☞ Total time, t₂ = 330 + 6 = 336 minutes

We know,

⇒ Time = Distance / Speed

Total time is given as 336 minutes

⇒ 260/x + 240/y = 336

As we have assumed, 1/x = a and 1/y = v,

⇒ 260a + 240b = 336

⇒ 130a + 120b = 168

⇒ 65a + 60b = 84 ...(2)

Multiply (1) by 3,

⇒ 90a + 60b = 99 ...(3)

Subtracting (2) from (3), we get

⇒ 90a + 60b - 65a - 60b = 99 - 84

⇒ 25a = 15

⇒ a = 15/25

⇒ a = 3/5

Put a = 3/5 in (1), we have

⇒ 30×3/5 + 20b = 33

⇒ 18 + 20b = 33

⇒ 20b = 15

⇒ b = 3/4

But we took, a = 1/x and b = 1/y

∴ x = 5/3 km/min and y = 4/3 km/min

Now, Let us convert the speed into m/s

⇒ x = 5/3 × 1000 / 60

⇒ x = 5/3 × 50/3

⇒ x = 250 / 9

⇒ x = 27.8 m/s

Also,

⇒ y = 4/3 × 1000/60

⇒ y = 4/3 × 50/3

⇒ y = 200/9

⇒ y = 22.2 m/s

Hence, The speed of the train is 27.8 m/s and that of the taxi is 22.2 m/s.

Answer 2

Answer:

✡ Given ✡

$\leadsto$ Abdul travelled 300 km by train and 200 km by taxi taking 5 hrs 30 mins.

$\leadsto$ But, if he travels 260 km by train and 240 km by taxi, he takes 6 min longer.

✡ To Find ✡

$\leadsto$ What is the speed of the train and that of the taxi.

✡ Solution ✡

✏ Let the speed of the train be x km/h

✏ And the speed of the taxi be y km/h

▶ According to the question,

➡ $\dfrac{300}{x}$ + $\dfrac{200}{y}$ = 5$\dfrac{1}{2}$

$\implies$ $\dfrac{300}{x}$ + $\dfrac{200}{y}$ = $\dfrac{11}{2}$ .. (1)

➡ $\dfrac{260}{x}$ + $\dfrac{240}{y}$ = ($\dfrac{11}{2}$ + $\dfrac{1}{10}$)

$\implies$ $\dfrac{260}{x}$ + $\dfrac{240}{y}$ = $\dfrac{56}{10}$ .. (2)

✏ Let $\dfrac{1}{x}$ = u and $\dfrac{1}{y}$ = v

$\therefore$ 300u + 200v = $\dfrac{11}{2}$ .. (3)

And, 260u + 240v = $\dfrac{56}{10}$

⬛ By solving the equation (3) and (4) we get,

$\mapsto$ u = $\dfrac{1}{100}$ $\implies$ x = 100 km/h

$\mapsto$ v = $\dfrac{1}{80}$ $\implies$ y = 80 km/h

Hence, the speed of the train and that of taxi are 100 km/h and 80 km/h respectively.

Step-by-step explanation:

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