Please someone help me
Answers
Let the speed of Train = x and speed of Car = y
In the qst case, A travels 400 kms by train and rest 600 - 400 = 200 kms by car. So, time taken to travel 600 kms
400/x + 200/y = 6 hrs 30 min = 6 1/2 hrs. = 13/2 hrs. …………… (1)
Similarly, in the 2nd case,
200/x + 400/y = 6 hrs 30 min + 30 min = 7 hrs…… (2)
Multiplying eqn (2) by 2 and subtracting from eqn (1), we get
400/x + 800/y - 400/x - 200/y = 7 * 2 - 13/2
Or, 600/y = 15/2
Or, y = 600 * 2 /15 = 80 km /hr
From eqn (2), we get
200/x + 400/80 = 7
Or, 200/x = 7 - 5 = 2
Or, x = 200/2 = 100 kms/hr
So, speed of the train = 100 kms/ he and that of car is 80 kms/hr.
Answer:
Let the speed of the train be ‘x’ km/hr and the speed of the car be ‘y’ km/hr.
It is given that he travels 400 km partly by train and the rest i.e. (600-400) = 200 km by car
To travels this distance he takes 6 hours 30 minutes which is equal to \left(6+\frac{30}{60}\right)=\frac{13}{2} \text { hours }(6+
60
30
)=
2
13
hours
Also it is given that he travels 200 km by train and the rest i.e. (600-200) = 400 km by car and the time taken is half an hour longer i.e. \left(\frac{13}{2}+\frac{1}{2}\right)=7 \text { hours }(
2
13
+
2
1
)=7 hours
Distance = Speed × Time
Now,
\frac{400}{x}+\frac{200}{y}=\frac{13}{2}
x
400
+
y
200
=
2
13
→ equation 1
\frac{200}{x}+\frac{400}{y}=7
x
200
+
y
400
=7 → equation 2
Multiplying Equation 2 with 2 we get
\frac{400}{x}+\frac{800}{y}=14
x
400
+
y
800
=14 → equation 3
Subtracting [Equation 3] from [Equation 2] we get,
\begin{gathered}\begin{array}{l}{\frac{600}{y}=14-\frac{13}{2}} \\\\ {\Rightarrow \frac{600}{y}=\frac{28-13}{2}} \\\\ {\Rightarrow \frac{600}{y}=\frac{15}{2}} \\\\ {\Rightarrow y=\frac{600 \times 2}{15}} \\\\ {\Rightarrow y=80 \mathrm{km} / \mathrm{hr}}\end{array}\end{gathered}
y
600
=14−
2
13
⇒
y
600
=
2
28−13
⇒
y
600
=
2
15
⇒y=
15
600×2
⇒y=80km/hr
Now substituting the value of y in [Equation 2] we get
\begin{gathered}\begin{array}{l}{\frac{200}{x}+\frac{400}{80}=7} \\\\ {\Rightarrow \frac{200}{x}+5=7} \\\\ {\Rightarrow \frac{200}{x}=7-5} \\\\ {\Rightarrow \frac{200}{x}=2} \\\\ {\Rightarrow x=\frac{200}{2}} \\\\ {\Rightarrow x=100}\end{array}\end{gathered}
x
200
+
80
400
=7
⇒
x
200
+5=7
⇒
x
200
=7−5
⇒
x
200
=2
⇒x=
2
200
⇒x=100
Thus the speed of the train is 100 km/hr and speed of the car is 80 km/hr.