Step 1: Understand the formula for Average Speed
The average speed for an entire journey involving different intervals is calculated using the total distance covered divided by the total time taken:
Average Speed=Total TimeTotal Distance
Step 2: Calculate the Total Distance
The journey is divided into two parts:
Total Distance=d1+d2=14+16=30 km
Step 3: Calculate the Total Time Taken
We know that Time=SpeedDistance. Let's find the time taken for each part:
Now, compute the total time (t1+t2):
Total Time=87+78
Take the Least Common Multiple (LCM) of 8 and 7, which is 56:
Total Time=56(7×7)+(8×8)=5649+64=56113 hours
Step 4: Calculate the Average Speed
Substitute the total distance and total time back into our main formula:
Average Speed=(56113)30
Average Speed=11330×56
Average Speed=1131680
Let us perform the division to find the approximate value:
Average Speed≈14.867 km/hr
Rounding off to two decimal places gives 14.86 km/hr.
Correct Answer
The correct option is (a) 14.86 km/hr.