A motor car travels 175 km distance from a place A to B,at a uniform speed 70km/hr passes though all ten green traffic signals.Due to heavy traffic it stops for 1 minute at first signal,3 minute at second signal,5 minute at third signal and so on stops for 19 minutseat tenth signal.How much total time it takes to reach at the place B.Solve by suitable mathematical method.
Time spent at signal
10/2(1+19)=100min----1
Speed = distance/time
Let time =x hr
70=175/x=
X=175/70=2.5hr
2.5hr =150min--2
Total time =150+100 min=250min
well,
S10 = 10/2 (1+19)
Answer
To find the total time it takes for the motor car to reach from place A to B, we need to consider both the time spent driving and the time spent waiting at traffic signals.
Let's first calculate the time spent driving:
The distance from place A to B is 175 km, and the car is traveling at a uniform speed of 70 km/hr. We can use the formula: time = distance / speed.
So, the time spent driving is: 175 km / 70 km/hr = 2.5 hours.
Now, let's calculate the total time spent waiting at the traffic signals:
The car passes through 10 traffic signals and stops at each one.
The waiting time at the signals is given as 1 minute, 3 minutes, 5 minutes, and so on, increasing by 2 minutes for each signal.
To find the waiting time at the tenth signal, we can use the formula: Nth term = a + (n-1) * d, where "a" is the first term, "n" is the number of terms, and "d" is the common difference.
In this sequence, the first term (a) is 1 minute, the number of terms (n) is 10, and the common difference (d) is 2 minutes.
So, the waiting time at the tenth signal is: 1 + (10-1) * 2 = 1 + 9 * 2 = 1 + 18 = 19 minutes.
Now, let's calculate the total time:
Total time = time spent driving + total waiting time
Total time = 2.5 hours + 19 minutes
To add minutes to hours, we need to convert minutes to hours.
There are 60 minutes in 1 hour, so 19 minutes is equal to 19/60 = 0.32 hours (approximately).
Total time = 2.5 hours + 0.32 hours = 2.82 hours.
Therefore, the total time it takes for the motor car to reach from place A to B is approximately 2.82 hours.