One dimensional motion!

From a town, cars start at regular intervals of 30 s and run towards a second town with a constant speed of 60 km/hr so that the time between their arrival is Δ t 1 \Delta t_1 . At some point of time, all of the cars leaving the first town reduce their speed to 40 km/hr due to bad weather conditions. What will be the time interval between consecutive cars reaching the second town after slowing down?

45s 20s 40s 30s

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1 solution

Remembering the basic formula: d i s t a n c e = v e l o c i t y × t i m e distance = velocity \times time

And knowing that the distance stays the same, we get: v e l o c i t y 1 × t i m e 1 = v e l o c i t y 2 × t i m e 2 velocity_{1} \times time_{1} = velocity_{2} \times time_{2} t i m e 2 = ( v e l o c i t y 1 × t i m e 1 ) / v e l o c i t y 2 time_{2} = (velocity_{1} \times time_{1} ) / velocity_{2} t i m e 2 = ( 60 k m / h r × 30 s ) / ( 40 k m / h r ) time_{2} = (60 km/hr \times 30 s) / (40 km/hr) t i m e 2 = 45 s time_{2} = \boxed{45 s}

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