During a trekking activity of 6km a student Ram will go to Sangam and return back up to 12 noon. He estimates that he can go to the Sangam at 1.5km/h on average, and return at half that speed. These speeds take into account breaks and rest times. Using Ram's estimated speeds, what is the latest time he can begin his walk so that he can return by 12 noon?
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Given:
Distance = 6 km
Time needed to be back = 12 noon
Speed going there = 1.5 km/h
Speed coming back = half the speed going there
To Find:
Latest time to leave for his walk
Solution
Find the distance one way:
One way = 6 ÷ 2
One way = 3 km
Find the speed coming back:
Speed coming back = half the speed going there
Speed coming back = 1/2 x 1.5 km/h
Speed coming back = 0.75 km/h
Find the time to go there:
Time = Distance ÷ Speed
Time = 3 ÷ 1.5
Time = 2 hours
Find the time needed to come back:
Time = Distance ÷ Speed
Time = 3 ÷ 0.75
Time = 4 hours
Find the total time:
Total time = 2 + 4
Total time = 6 hours
Find the latest time he must leave for his walk:
Latest time = 12 noon - 6 hours before
Latest time = 6 am
Answer: He needs to leave at 6 am
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