Question
Ajay and Bharti are initially 493 km apart. They start
jogging towards each other with speeds of 36 km/h and 64 km/h, respectively, at the same time. If Ajay increases his speed by 6 km/h every hour and Bharti decreases her speed by 4 km/h every hour, find the time it takes for them to meet.Solution
ATQ, Relative speed = 36 + 64 = 100 km/h Relative speed increases by 2 km/h (6 – 4 = 2) every hour Let they meet after ‘t’ hours, Relative speed in 1st hour = 100 km/h Relative speed in 2nd hour = 102 km/h So, relative speed will be as 100 km/h, 102 km/h, 104 km/h, 106 km/h, 108 km/h ........ Distance travelled in 4 hours = 100 + 102 + 104 + 106 = 412 km Distance remaining = 493 – 412 = 81 km Relative speed in 5th hour = 108 km/h Hence, desired time = 4 + 81/108 = 4.75 hours = 4 hours 45 minutes
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