A motor boat whose speed is 18 km/h in still water. It takes 1 hour more to go
24 km upstream than to return downstream to the same spot. Find the speed of the stream.
Solution :
Let the speed of the stream be x km/h.
Therefore, the speed of the boat upstream = (18 – x) km/h and the speed of the boat
downstream = (18 + x) km/h.
The time taken to go upstream =
distance
speed =
24
18 - x
hours.
Similarly, the time taken to go downstream =
24
18 + x
hours.
According to the question,
24 24 1
18 18
- =
- + x x
i.e., 24(18 + x) – 24(18 – x) = (18 – x) (18 + x)
i.e., x
2
+ 48x – 324 = 0
Using the quadratic formula, we get
2
48 48 1296 48 3600
2 2
-± + -±
x = =
48 60 6
2
- ±
= = or -54
Since x is the speed of the stream, it cannot be negative. So, we ignore the root x = – 54.
Therefore, x = 6 gives the speed of the stream as 6 km/h.
EXERCISE - 5.3
1. Find the roots of the following quadratic equations, if they exist.
i. 2x
2
+ x – 4 = 0 ii. 2
4 43 3 0
iii. 5x
2
- 7x - 6 = 0
iv.x²+5=-6
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