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.
It's urgent.
Answers
Explanation.
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.
Explanation:
Step-by-step explanation:
Given that:Abdul travelled 300km by trains and 200km by taxi, it took 5 hours 30 minutes.but ifhe travels 260km by train and 240 km by taxi,he takes 6 minutes longer.
To find: find the speed of the train and that of the taxi.
solution: Let the speed of train is x km/hr
and speed of taxi is y km/hr
Since,Travelling time is given in both the cases,calculate the time taken by train and by taxi and form linear equations
Case1: Abdul travelled 300km by trains and 200km by taxi, it took 5 hours 30 minutes.
Time taken by train to cover 300 km with the speed x km/hr
Time= Distance travelled/speed
= 300/x hr
Time taken by taki to travel 200 km,
= 200/y
$$\begin{lgathered}\frac{300}{x} + \frac{200}{y} = \frac{11}{2} \: \: \: \: eq1\\\end{lgathered}$$
Case2: Abdul travels 260km by train and 240 km by taxi,he takes 6 minutes longer..
Time taken by train to cover 260 km with the speed x km/hr
Time= Distance travelled/speed
= 260/x hr
Time taken by taki to travel 240 km,
= 240/y
$$\begin{lgathered}\frac{260}{x} + \frac{240}{y} = 5 \: hr \: 36 \: min \\ \\ \frac{260}{x} + \frac{240}{y} = 5 \frac{36}{60} \\ \\ \frac{260}{x} + \frac{240}{y} = 5 \frac{3}{5} \\ \\ \frac{260}{x} + \frac{240}{y} = \frac{28}{5} \: \: \: \: \: eq2 \\ \\\end{lgathered}$$
Eq1 and 2 can be converted to linear equation
$$\begin{lgathered}let \\ \\ \frac{1}{x} = a \\ \\ \frac{1}{y} = b \\ \\ 300a + 200b = \frac{11}{2} \: \: \: \: ...eq3\\ \\ 65a + 60b = \frac{7}{5} \: \: \:... eq4 \\ \\\end{lgathered}$$
On solving these linear equations by elimination method,
Multiply eq3 by 60 and eq4 by 200 and subtract both
$$\begin{lgathered}60[300a + 200b = \frac{11}{2}]\\\\18000a+12000b=330 \: \: \: \: ...eq5\\ \\ 200[65a + 60b = \frac{7}{5}]\\\\ 13000a+12000b=280 \: \: \:... eq6\\ \\\end{lgathered}$$
Eq5-eq6
$$\begin{lgathered}5000a=50\\\\a=\frac{50}{5000}\\\\a=\frac{1}{100}\\\\\end{lgathered}$$
put the value of a in eq 4
b= 1/80
Now
$$\begin{lgathered}a = \frac{1}{100} \\ \\ b = \frac{1}{80} \\ \\\end{lgathered}$$
Thus,
Thus,the speed of train is 100km/hr and speed of taxi is 80 km/hr.
Hope it helps you.