Boat takes 8 hours to rope 48 km downstream in 12 hours to row the same distance upstream .find the boats rate in still water and rate of the current
Answers
Step-by-step explanation:
boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
A. 8 : 3 B. 5 : 6
C. 3 : 8 D. 6 : 5
Answer: Option A
Explanation:
Let the rate upstream of the boat
=
x
kmph
and the rate downstream of the boat
=
y
kmph
Distance travelled upstream in 8 hrs 48 min = Distance travelled downstream in 4 hrs.
Since distance = speed × time, we have
x
×
8
4
5
=
y
×
4
x
×
44
5
=
y
×
4
x
×
11
5
=
y
⋯
(equation 1)
Now consider the formula given below
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water
=
1
2
(
a
+
b
)
km/hr
Rate of stream
=
1
2
(
a
−
b
)
km/hr
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Hence, speed of the boat
=
y
+
x
2
speed of the water
=
y
−
x
2
Required Ratio
=
(
y
+
x
2
)
:
(
y
−
x
2
)
=
(
y
+
x
)
:
(
y
−
x
)
=
(
11
x
5
+
x
)
:
(
11
x
5
−
x
)
(∵ Substituted value of
y
from equation 1)
=
(
11
x
+
5
x
)
:
(
11
x
−
5
x
)
=
16
x
:
6
x
=
8
:
3