Data Sufficiency

lheiannie07 wrote:Mark biked from his house to his friend's house in how many hours?

(1) Mark bikes at an average speed of 72 blocks per hour.

(2) If Mark could bike an extra 8 blocks for each hour, he would have arrived at his friend's place 1 hour earlier

Let t = the number of hours.

Statement 1:
Since the distance can be any positive value, the value of t cannot be determined.
INSUFFICIENT.

Statement 2:
Case 1: r = 72 blocks per hour, implying that d = 72t
If the rate increases by 8 blocks per hour to 80 blocks per hour, Mark takes 1 fewer hour to travel the same distance:
d = (80)(t -1) = 80t - 80.
Since the expressions in blue represent the same distance, they must be EQUAL:
72t = 80t - 80
80 = 8t
t = 10.

Case 2: r = 80 blocks per hour, implying that d = 80t
If the rate increases by 8 blocks per hour to 88 blocks per hour, Mark takes 1 fewer hour less to travel the same distance:
d = (88)(t -1) = 88t - 88.
Since the expressions in blue represent the same distance, they must be EQUAL:
80t = 88t - 88
88 = 8t
t = 11.

Since t can be different values, INSUFFICIENT.

Statements combined:
Only Case 1 satisfies both statements.
Thus, t=10.
SUFFICIENT.

The correct answer is C.