A bike rider increases his speed by 1 km/hr after every 30 minutes. if the distance travelled in the first half an hour is 30 km, what is the distance covered in 5 hours?
Answers
Answer:
Distance covered in 5 hours = 322.5 km
Step-by-step explanation:
In the total time of five hours, there will be 10 intervals of 30 minutes each.
In the first interval
Distance = 30 km
Time = 30 minutes = 0.5 hours
Speed = Distance / Time
= 30 / 0.5
= 60 km per hour
In the second interval of 30 minutes
Speed = 60 km per hour + 1 km per hour
= 61 km per hour
Distance = Speed * Time
= 61 * 0.5
= (60 + 1)*0.5
= 30 + 0.5
= 30.5 km
The distance gained by increasing speed by 1 km per hour in every interval = 0.5 km
Hence, for third interval
Distance = 30.5 km + 0.5 km
= 31 km
And so on...
Total distance travelled in 10 intervals is:
30 + 30.5 + 31 + 31.5 + 32 + 32.5 + 33 + 33.5 + 34 + 34.5
= 322.5
Total distance travelled in 5 hours = 322.5 km
Please note that:
30 + 30.5 + 31 + 31.5 + 32 + 32.5 + 33 + 33.5 + 34 + 34.5
is sum of AP where
number of terms = n = 10
first term = 30
last term = 34.5
Sum of AP = (n/2)*[first term + last term]
= (10/2)*(30 + 34.5)
= 5*64.5
= 322.5