A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30 km upstream and 21 km downstream in 6.5 hrs. Find the speed of the boat in still water and also speed of the stream.
Answers
SOLUTION :
Let the speed of the boat in still water be x km/hr and the speed of the stream be y km/hr the
Speed upstream = (x-y)km/hr
Sped down stream= (x+y)km/ hr
Case : 1
Time taken to cover 28 km downstream = 28/(x+y) hrs
[ Time = distance/speed]
Time taken to cover 24 km upstream = 24/(x−y) hrs
Given : The total time of journey = 6 hours
24/(x−y) + 28/(x+y) = 6 ………..…(1)
Case : 2
Time taken to cover 30 km upstream =30/(x−y)
Time taken to cover 21 km downstream =21/(x+y)
Given : The total time of journey = 6.5 hrs
30/(x−y) + 21(x+y) = 13/2………….(2)
Putting 1/(x−y) and 1/(x+y) in equation (1) and (2)
24u + 28v - 6 = 0 ………….…(3)
30u + 21v – 6.5 = 0 ………....(4)
Solving these equations by cross multiplication we get,
u/28 × - 6.5 − 21× −6 = −v/ 24×−6.5 − 30× -6 = 1/ 24×21−30×28
u/ -182 +126 = -v / - 156 + 180 = 1/504 - 840
u /- 56 = -v/24 = 1/ - 336
u / -56 = 1/ - 336
u = 56/336
u = 1/6
-v/24 = 1/ - 336
v = 24/336
v = 1/14
Now,
1/(x−y) = u
1/(x−y) = 1/6
x - y = 6………….(5)
1/(x+y) = v
1/(x+y)= 1/14
x + y = 14………....(6)
On adding eq 5 & 6,
x - y = 6
x + y = 14
--------------
2x = 20
x = 20/2
x= 10
On putting x = 10 in equation,5 we get,
x - y = 6
10 - y = 6
10 - 6 = y
y = 4
Hence,Speed of the stream = 4km/hr & Speed of boat = 10km/hr.
HOPE THIS ANSWER WILL HELP YOU….
Answer:
A boat goes 24 km upstream and 28 km downstream in 6 hours. In 6.5 hours , it can go 30 km upstream and 21 km downstream. Find the speed of the stream and the speed of the boat in still water.
Step-by-step explanation