Question

0.45
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​

Answer 1

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,...