Subject:
MathAuthor:
rihannabyrdCreated:
1 year agoAnswer:
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Author:
midnightqaso
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4Q- A jogger is training for a 5 km charity run. He starts with a run of 400 m then he increases the distance he runs by 200 m each day. How many days does it take the jogger to reach a distance of 5 km in training? What total distance will he have run in training by then?
Given,
Total distance = 5km
The distance covered on the first day = 400m
He increases the distance he runs by 200 m each day
To Find,
Days taken to reach a distance of 5km =?
The total distance will he have run in training by then =?
Solution,
The distance covered on the first day = 400m
The distance covered on the second day = 400m + 200 = 600m
The distance covered on the third day = 600m + 200m = 800m
This is an AP as difference between each day is same.
Therefore, a = 400m and common difference = 200m
According to the question, nth term of AP = 5k = 5000m
By the formula of the nth term in AP, we have
[tex]a_n = a + (n-1)d\\5000 = 400 + (n-1)*200\\5000 - 400= (n-1)*200\\4600/200= (n-1)\\23 + 1 = n\\n =24[/tex]
Days taken to reach a distance of 5km = 24 days
The total distance will he have run in training by then = The sum up to the nth term in the AP
[tex]S_n = (n / 2)(2a + (n-1)d)\\S_n = (24 / 2)(2*400 + (24-1)200)\\S_n = 12*(800 + 23*200)\\S_n = 12*(800 + 4600)\\S_n = 12*5400\\S_n = 64800[/tex]
Hence, the jogger will take 24 days to reach a distance of 5 km in training. He will have run 64800(64.8km) in training by then.
Author:
shermankwhc
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