- A takes 3 h more than B in walking 30 km. If A doubles his speed, he will take 2 h less than B.
Assuming the speed of A to be x km/h, obtain an equation. Also, find the speeds of A and B.
Answers
Answer:
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Step-by-step explanation:
Let the speed of A and B be x km/hr and y km/hr
Time taken by A to cover 30km
x
30
hrs
Time taken by B to cover 30km
y
30
hrs
According to the question
⇒
x
30
−
y
30
=3
⇒
x
10
−
y
10
=1...eq1
If A double his pace then the speed of A is 2x km/hr
therefore time taken by A to cover the 30 = 30/2xhrs And time taken by B to cover the 30KM = 30/yhrs
Now according to the question
⇒
y
30
−
2x
30
=
2
3
⇒
y
10
−
x
5
=
2
1
⇒−
x
10
+
y
20
=1...eq2
Now we assume
x
1
=u and
y
1
=v
Putting the u and v in eq1 and eq 2 we get
⇒10u−10v=1...eq3
⇒−10u+20v=1...eq4
Adding eq3 and eq4 we get
⇒10v=2
⇒v=
10
2
⇒v=
5
1
=
y
1
→y=5
Put v=
5
1
in eq3
⇒10u−3=0
⇒u=
10
3
=
x
1
⇒x=
3
10
Hence, the speed of A = 10\3 km/hr
The speed of B=5 km/hr respectively