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.
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.
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