Question
A cyclist moves at 25 km/h to
reach a checkpoint on time. If the speed is increased to 30 km/h, the cyclist will arrive 12 minutes earlier. Find the time taken to cover thrice the distance at 40 km/h.Solution
ATQ, Let the usual time taken by the cyclist be 'T' hours. Using, distance = speed × time We have, 'D' = 25T ----------- (I) And, 'D' = 30 × {T - (12/60)} -------- (II) From equation (I) and (II), We have, 25T = 30 × {T - (12/60)} Or, 25T = 30T - 30 × (12/60) Or, 5T = 6 Or, 'T' = 1.2 On putting the value of 'T' = 1.2 in equation (I), We have 'D' = 25 × 1.2 = 30 km So, the required time = (3 × 30) ÷ 40 = (90/40) = 2.25 hours
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