A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water
Solution:
We will use the formula speed = distance / time to find the speed of the boat in still water.
Let the speed of the boat in still water be x km/h and the speed of the stream be y km/ h.
As we know that the speed of the boat in downstream water is (x + y)km/h.
Similarly the speed of the boat in upstream water is (x - y) km/h.
Given,
Time taken by the boat to go 30km upstream and 44km downstream is 10 hours.
Using the speed formula
⇒ be equation (1)
Time taken by the boat to go 40km upstream and 55km downstream is 13 hours.
Using the speed formula
⇒ be equation (2)
Let 1/ (x - y) be a and 1/ (x + y) be b.
Substitute the values of in equation (1) and (2), we get
⇒ 30a + 44b = 10 be equation (3)
⇒ 40a + 55b = 13 be equation (4)
We will use elimination method to solve the equation.
Multiply equation (3) by 4 and equation (4) by 3.
⇒ 120a + 176b = 40 be equation (5)
⇒ 120a + 165b = 39 be equation (6)
Subtract equation (6) from equation (5)
⇒ (120a + 176b = 40) - (120a + 165b = 39)
11b = 1 ⇒ b = 1/11
Substitute the value of b in equation (3).
⇒ 30a + 44(1/11) = 10
⇒ 30a = 10 - 4
⇒ a = 6/30 ⇒ a = 1/5
∵ a = 1/5 ; b = 1/11
By substituting the values a and b
⇒ 1/(x - y) = a and 1/(x + y) = b
⇒ 1/(x - y) = 1/ 5 and 1/(x + y) = 1/11
⇒ x - y = 5 be equation (7)
and x + y = 11 be equation (8)
Add equation (7) and (8)
⇒ 2x = 16 ⇒ x = 8
Substitute the value of x in equation (7).
⇒ x - y = 5
⇒ 8 - y = 5
⇒ y = 3
∴ x = 8; y = 3
Thus, the speed of the boat is 8 km/h in still water and 3 km/ h is the speed of the stream
☛ Check: NCERT Solutions for Class 10 Maths Chapter 3
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water
Summary:
The speed of the boat in still water is 8 km/ h and the speed of the stream is 3km/ h when a boat goes 30 km upstream and 44 km downstream in 10 hours and in 13 hours, it can go 40 km upstream and 55 km down-stream
☛ Related Questions:
- The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?
- Solve the pair of equations: 2/x + 3/y = 13, 5/x - 4/y = -2
- Solve the following pair of equations by reducing them to a pair of linear equations: 5 / (x -1) + 1 / (y - 2) = 2, 6 / (x - 1) - 3 / (y - 2) = 1
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