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downstream in 612 hrs. Find the speed of the boat in still water and also speed of the stream
X takes 3 hours more than Y to walk 30 km. But, if X doubles his pace, he is ahead of Y by 12 hours.
Find their speed of walking.
201
Answers
Answer:
Let the speed of X and Y be x km/hr and y km/hr respectively. Then,
Time taken by X to cover 30km =
x
30
hrs,
and, Time taken by Y to cover 30km =
y
30
hrs
By the given conditions, we have
x
30
−
y
30
=3⇒
x
10
−
y
10
=1 .(i)
If X doubles his pace, then speed of X is 2x km/hr
Times taken by X to cover 30 km =
2x
30
hrs
Times taken by Y to cover 30km = y30hrs
According to the given conditions, we have
y30 − 2x30 =1 +2/1
⇒ y30− 2x30 = 2/3
⇒ y10 − x5 = 2/1
⇒ − x10 + y20 =1
(i)Putting x 1 =u and y1 =v, in equations (i) and (ii)
we get,
10u−10v=1⇒10u−10v−1=0 (iii)
−10u+20v=1⇒−10u+20v−1=0 (iv)
Adding equations (iii) and (iv), we get
10v−2=0⇒v= 5/1
(ii)Putting v= 5/1
in equation (iii), we get
10u−3=0⇒u= 10
Now, u= 10/3
⇒ x1 = 10/3
⇒x= 3/10 and, v= 5/1
⇒ y1= 5/1
⇒y=5
Hence, X's speed = 3/10
10 km/hr and, Y's speed =5 km/hr.
I hope it will helpful,...