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Question

A motor car travels 175 distance from a place A to place B, at a uniform speed 70km/hr passes though all ten green traffic signals. Due to heavy traffic it stops for one minute at first signal, 3 minutes at second signal, 5 minutes at third signal and so on stops for 19 minutes at tenth signal. How much total time it takes to reach at the place B. Solve by suitable mathematical method.

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Solution

Time taken to travel from A to B excluding stops can be found using the formula: time=DistanceSpeed
On solving, tt=17570 hr
tt=17570×60 min
tt=150 min

Now, stop time at first signal is t1=1 s
at second signal is t2=3 s and so on
This forms an arithmetic progression with first term a1=1, common difference d=2, number of terms n=10
Total stop time is the sum of this series. Hence,
ts=n2(2a1+(n1)d)
ts=102(2×1+(101)×2)
ts=100 min

Total travel time equals the sum of stop time and travel time.
t=ts+tt
t=100+150
t=250 min=4 hr 10 min

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