Q1 Swati can row her boat at a speed of 5 km/h in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream. Q2 Q.32. A person on tour has Rs 360 for his expenses. If he extends his tour for four days, he has to cut down his daily expenses by Rs 3. Find the original duration of the tour.
Answers
Answered by
174
Q1 Solution:
Let the speed of the stream be x km/h
Speed of boat upstream =(5-x) km/h
speed of boat downstream = (5+x) km/h
Time taken to go upstream =5.25/(5-x).
Time taken to go downstream = 5.25/(5+x).
Time = distance / speed.
from the question we can write
[5.25/(5-x)] -[5.25/(5+x)]=1
5.25(5+x) - 5.25(5-x)=(5+x)(5-x)
10.5x=25-x²
x²+10.5x-25=0
(x-2)(x+12.5)=0
∴ x=2 and x= -12.5
(discarding the negative value)
x=2 km/h is the speed of the stream.
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Q2 solution:
Let original duration of tour = x days.
Total expenses = Rs 360
Duration of tour extended = (x+4) days.
extended tour expenses per day =360/(x+4)
expenses per day =360/x
Given that expenses per day is cut by rs 3
((360/x)-(360/(x+4))=3
360(x+4)-360 x=3(x(x+4))
3x²+12x-1440=0
3(x+24)(x-20)=0
x=-24 and x=20
Discarding the negative value
we get x=20.
So the original duration of the tour was 20 days.
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Let the speed of the stream be x km/h
Speed of boat upstream =(5-x) km/h
speed of boat downstream = (5+x) km/h
Time taken to go upstream =5.25/(5-x).
Time taken to go downstream = 5.25/(5+x).
Time = distance / speed.
from the question we can write
[5.25/(5-x)] -[5.25/(5+x)]=1
5.25(5+x) - 5.25(5-x)=(5+x)(5-x)
10.5x=25-x²
x²+10.5x-25=0
(x-2)(x+12.5)=0
∴ x=2 and x= -12.5
(discarding the negative value)
x=2 km/h is the speed of the stream.
------------------------------------------------------------------------------------------------------
Q2 solution:
Let original duration of tour = x days.
Total expenses = Rs 360
Duration of tour extended = (x+4) days.
extended tour expenses per day =360/(x+4)
expenses per day =360/x
Given that expenses per day is cut by rs 3
((360/x)-(360/(x+4))=3
360(x+4)-360 x=3(x(x+4))
3x²+12x-1440=0
3(x+24)(x-20)=0
x=-24 and x=20
Discarding the negative value
we get x=20.
So the original duration of the tour was 20 days.
========================================================
Answered by
53
Answer:
Step-by-step explanation:
Speed of boat in still water = 5 km/h
Let speed of stream be 'x' km/h.
Speed of boat in upstream = (5 - x) km/h
Speed of boat in downstream = (5 + x) km/h
Distance travelled by boat in upstream = Distance travelled by boat in downstream = 5.25 km
ATQ:-
5.25(1/5-x - 1/5+x) = 1
=> 5.25 ( 2x/25 - x2) = 1
=> 10.5x = 25 - x2
=> x2 +10.5x - 25 = 0
=> (x+12.5)(x-2) = 0
=> x = 2 or x = -12.5
x can't be -12.5 as speed can't be negative
Therefore, Speed of stream is 2 km/h.
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