A bicycle rider coasts down the hill, travelling 4ft in the first seco

Question

A bicycle rider coasts down the hill, travelling 4ft in the first second. In each succeeding second, he travels 5ft farther than in the preceeding second. If the rider reaches the bottom of the hill in 11 seconds, find the total distance travelled.

A. 54
B. 304
C. 309
D. 314
E. 319

A. 54
B. 304
C. 309
D. 314
E. 319

firas92 · Accepted Answer

We have an arithmetic sequence with first term  a_1=4  and common difference  d=5

The 11th term  a_{11}=a_1+(11-1)*d = 4+50=54

Sum of terms  = \frac{n}{2}(a_1+a_{11}) = \frac{11}{2}(4+54) = 319

Answer is  (E)

Skate · Answer

Distance traveled at 11th sec = Distance traveled at 1st sec + (11-1) * 5 = 54
Sum = 11/2 * (1st + 11th) = 11/2 * (4+54) = 319
Answer: E

Kinshook · Answer

Given: A bicycle rider coasts down the hill, travelling 4ft in the first second. In each succeeding second, he travels 5ft farther than in the preceeding second. The rider reaches the bottom of the hill in 11 seconds.

Asked: Find the total distance travelled.

The distance travelled in first second = 4 m = 5-1 ft
The distance travelled in second second = 4 + 5 ft = 5*2 -1 ft = 9ft
In general
The distance travelled in nth second = 5n -1 ft
Total distance travelle in n seconds = 5n(n+1)/2 - n ft
Sum of 11 terms of the sequence = 5*11*12/2 - 11 = 30*11 -11 = 29*11 = 319 ft
Total distance travelled.= 319 ft

IMO E

sarphant · Answer

Check the pattern -
!st sec - 4ft.
2nd - 4+5
3rd - 4+2*5
....
11th - 4+10.5

So Total = 44+(1+2+3+4.....10)*5 = 319.

effatara · Answer

I guess we could shave off a few seconds by eliminating the step of calculating the distance traveled in the 11th second and directly applying the formula for 'Sum of an Arithmetic Series':
Sn=(n/2){2a+(n-1)d} where 'n' is the number of terms, 'a' is the 1st term and 'd' is the Common Difference (difference between one term and the next).
Total distance traveled = (11/2){2*4+(11-1)*5} = 319 ANS: E

Any time saving, however small, helps!

ScottTargetTestPrep · Answer

We can use the formula sum = avg x quantity

avg = (4 + 4 + 5 x 10)/2 = 58/2 = 29

Thus, the distance traveled was 29 x 11 = 319 ft.

Answer: E

btsaami · Answer

Let speed in 1st second be 4ft/sec, in second 4+5 ft/sec, 3rd 4+5*2 ft/sec

Speed * Time = Distance
As the speed is integer and from the options distance will also be an integer and multiple of 11.

Other concept : Time is constant, avg of the speed will be AM. Sum = Avg*n = Integer

Checking all the options, we see that only 319 satisfies to be an answer.

Note: This method can be used when time is very less and is only specific to this sum.

A bicycle rider coasts down the hill, travelling 4ft in the first seco

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