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.

Answer 1

Time taken to travel from $A$ to $B$ excluding stops can be found using the formula: $\text{time}=\frac{\text{Distance}}{\text{Speed}}$

On solving, $t_t=\frac{175}{70}hr$

$t_t=\frac{175}{70}\times 60min$

$t_t=150min$

Now, stop time at first signal is $t_1=1s$

at second signal is $t_2=3s$ and so on

This forms an arithmetic progression with first term $a_1=1$, common difference $d=2$, number of terms $n=10$

Total stop time is the sum of this series. Hence,

$t_s=\frac{n}{2}(2a_1+(n-1\left)d\right)$

$t_s=\frac{10}{2}(2\times 1+(10-1)\times 2)$

$t_s=100min$

Total travel time equals the sum of stop time and travel time.

$t=t_s+t_t$

$t=100+150$

$t=250min=4hr10min$