Question
'R' started his journey from point 'X' towards point 'Y' at
40 km/h. Three hours later, 'S' left point 'X' towards point 'Y' at 70 km/h. 'T' left point 'X' towards 'Y' after 'M' hours of 'R's journey at 105 km/h. If both 'S' and 'T' overtook 'R' at the same time, find the value of M.Solution
ATQ,
Distance covered by 'R' in the first three hours = 40 × 3 = 120 km
Relative speed of 'S' with respect to 'R' = 70 − 40 = 30 km/h
Time taken by 'S' to overtake 'R' = 120 ÷ 30 = 4 hours
Distance covered by 'S' in 4 hours = 70 × 4 = 280 km
Time taken by 'T' to cover 280 km = 280 ÷ 105 = 2.67 hours
So, 'T' must have left 2.67 hours before 'S' overtook 'R', i.e., 4 − 2.67 = 1.33 hours after 'S' left
Therefore, M = 3 + 1.33 = 4.33 hours
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