if the time taken by the boat to cover 60 km upstream and 100 km downstream in 20 hours find the time taken by the boat to cover 15 km upstream and 25 km downstream?
1)4 hours
2)6 hours
3)8 hours
4)5 hours
Answers
Answer:
5 hours
Step-by-step explanation:
Given:
Time taken by boat to cover 20 km upstream and 60 km downstream = 5 hrs.
Time taken by boat to cover 60 km upstream and 80 km downstream = 7 hrs.
Concept Used:
If 'b' is the speed of a boat and 's' is the speed of a stream then,
Upstream speed of boat = b - s
& Downstream speed of boat = b + s
Calculation:
Let the speed of the boat be 'b' and the speed of the stream be 's'.
According to the question,
(20/(b-s)} + {60/(b + s)} = 5
(30/(b-s)} + {80/(b + s)} = 7
-(0)
Let us put 1/(b-s) =P and 1/(b + s) = Q in equation (i) and (ii),
So,
20P +60Q = 5
30P + 80Q = 7
Multiplying equation (iii) by 3 and equation (iv) by 2, we get
60P + 180Q = 15 ----(v)
60P + 160Q = 14 ---(vi)
Solving these we get,
(180-160)Q = 15-14
⇒ 20Q = 1
⇒ Q = 1/20
So, P = {5-60 x (1/20))/20
⇒P= {5- (60/20)}/20
⇒P=(5-3)/20
⇒P=2/20
⇒P=1/10
So, b - s = 10 & b + s = 20
So, b = 15 km/hr and s = 5 km/hr.