SOLUTION: A tugboat goes 120 miles upstream in 20 hours. The return trip downstream takes 5 hours. Find the speed of the tug boat without a current , and with a current.
Question 635052: A tugboat goes 120 miles upstream in 20 hours. The return trip downstream takes 5 hours. Find the speed of the tug boat without a current , and with a current. Answer by Maths68(1474) (Show Source):
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Speed of boat without current
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Time=t=20 hours
Speed of boat= s =
Distance = d = 120 miles
Speed of current = c
Distance=(Speed of boat - Speed of current) *time
120=(s-c)*20
120/20=s-c
6=s-c
s-c=6………………………….(1)
Speed of boat with the current
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Time=t=5 hours
Speed = s =
Distance = d = 120 miles
Speed of current = c
Distance=(Speed of boat+ Speed of current) *time
120=(s+c)*5
120/5=s+c
24=s+c
s+c=24………………………………………(2)
Add (1) and (2)
s-c=6……………………………………….(1)
s+c=24………………………………………(2)
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2s=30
s=30/2
s=15
Speed of boat is 15miles/hour.
Put the value of s in (1)
s-c=6……………………………………….(1)
15-c=6
-c=6-15
-c=-9
c=9
Speed of current is 9miles/hour.
Speed of boat without current = 15-9 = 6miles/hour
Speed of boat with current = 15+9=24miles/hour
Check
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120 miles in 20 hours upstream
time*speed= distance
time=distance/speed
time=120/6=20hours
120 miles in 5 hours downstream
time*speed= distance
time=distance/speed
time=120/24=5hours
