As per the first given condition,
Let the speed of the boat in still water be x km/hr and the speed of the stream be y km/hr.
(Q)
Sol.
What we need to find?
A boat takes 6 hours to travel 8 km upstream and 32 km downstream, and it takes 7 hours to travel 20 km upstream and 16 km downstream.
Find the speed of the boat in still water and the speed of the stream.
Let us assume that
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Upstream
Downstream
Distance
8 km
32 km
Speed
Speed of boat in upstream will be (x – y) km/hr
Speed of boat in downstream will be (x + y) km/hr
(x – y) km/hr
(x + y) km/hr
Time
We know that
hrs
hrs
Total time is 6 hours
+
=
6
........(i)
20 km
16 km
Total time is 7 hours
As per the second given condition,
+
=
7
........(ii)
(Q)
Sol.
A boat takes 6 hours to travel 8 km upstream and 32 km downstream, and it takes 7 hours to travel 20 km upstream and 16 km downstream.
Find the speed of the boat in still water and the speed of the stream.
+
=
6
........(i)
+
=
7
........(ii)
8m + 32n = 6
20m + 16n = 7
…. (iii)
…. (iv)
Multiplying (iv) by 2, we get
40m + 32n = 14
…. (v)
Subtracting (iii) from (v)
40m + 32n = 14
8m + 32n = 6
32m
(–) (–) (–)
= 8
8
+ 32n
= 6
∴
2 + 32n
= 6
∴
32n
= 6 – 2
∴
32n
= 4
∴
n
∴
n
Resubstituting the values of m and n we get,
= 4 ….(vi)
= 8 ….(vii)
Adding (vi) and (vii),
x – y = 4
x + y = 8
2x = 12
∴ x = 6
Substituting x = 6 in (vii)
6
∴
y
∴
y = 2
∴ The speed of boat in still water is 6km/hr and speed of stream is 2km/hr
+
y
=
8
=
8
–
6