Question

how many hours would it take for a biker to travel 54 km if the first are you travelled 15 km and each subsequent hour he travelled 1 km less than the hour before​

Answer 1

Where's the problem bro, you have already got the correct answer

Answer 2

Answer:

It will take 4 hours for a biker to travel 54 km

Step-by-step explanation:

The first hour you traveled 15 km and each subsequent hour he traveled 1 km less than the hour before​

So, AP : 15,14,13,......

first term = a = 15

d = common difference = -1 km

n = no. of hours

Now we are supposed to find how many hours would it take for a biker to travel 54 km

Formula of sum of first n terms = $S_n=\frac{n}{2}(2a+(n-1)d)$

$54=\frac{n}{2}(2(15)+(n-1)(-1))$

$54=\frac{n}{2}(30-n+1)$

$108=n(31+n)$

$108=-n^2+31n$

$n^2-31n+108=0$

$n^2-27n-4n+108=0$

$n(n-27)-4(n-27)=0$

$(n-4)(n-27)=0$

$n = 4,27$

At n = 4

$S_n=\frac{4}{2}(2(15)+(4-1)(-1))$

$S_n=54$

So,  it will take 4 hours for a biker to travel 54 km