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What is the time after which the boat must turn around in the following problem:A boat...
What is the time after which the boat must turn around in the following problem:
A boat travels at at 20 km/h in still water. The current in a river flows at 5 km/h. The boat has enough fuel for 3 hours. It leaves its base and travels downstream. When should it turn around to be able to return to its base. Also, provide a distance-time graph.
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The boat travels at 20 km/h in still water. When it leaves its base it travels downwards. As the river flows at 5 km/h, the speed of the boat downstream is 25 km/h. The speed of the boat upstream is 15 km/h.
Let the time when the boat has to turn around be T hours after starting. The distance traveled downstream is 25*T. After turning around the distance travels upstream is 15*(3 - T). These have to be equal to allow the boat to return back.
25*T = 45 - 15*T
=> 40*T = 45
=> T = 45/40 hours
The distance-time graph as it travels downstream and upstream is:
The red line shows the journey downstream and the green line shows the journey upstream.
The boat should turn back after 1.125 hours.
Posted by justaguide on December 22, 2011 at 11:21 PM (Answer #3)
Speed of boat downstream is 20 + 5 = 25 km/hr
Speed of boat upstream is 20 - 5 = 15 km/hr
Time downstream = Distance Downstream/25
Time upstream = return distance (same as Distance Downstream)/15
Time downstream + Time upstream = 3 hours.
Therefore D/25 + D/15 = 3
Multiply both sides by 225, giving 9D + 15D = 675
24D = 675
D = 28.12
Time downstream = 28.12/25 = 1.12 hrs.
So he should turn around after going downstream for 1.12 hours.
See first answer for a distance/time graph.
Posted by boblawrence on December 23, 2011 at 6:29 AM (Answer #4)
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