## Is the number of seconds required…

## Solution:

We need to determine whether the number of seconds required to travel d_1 feet at r_1 feet per second is greater than the number of seconds required to travel d_2 feet at r_2 feet per second. We can set this question up in the form of an inequality. Remember that:

time = distance/rate

Thus, we can now ask:

Is d_1/r_1 > d_2/r_2 ?

When we cross multiply we obtain:

Is (d_1)(r_2) > (d_2)(r_1) ?

**Statement One Alone: **

d_1 is 30 greater than d_2.

From statement one, we can create the following equation:

d_1 = 30 + d_2

Since d_1 = 30 + d_2, we can substitute 30 + d_2 in for d_1 in the inequality (d_1)(r_2) > (d_2)(r_1):

Is (30 + d_2)(r_2) > (d_2)(r_1) ?

We see that we still cannot answer the question. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

**Statement Two Alone: **

r_1 is 30 greater than r_2.

From statement two we can create the following equation:

r_1 = 30 + r_2

Since r_1 = 30 + r_2, we can substitute 30 + r_2 for r_1 in the inequality (d_1)(r_2) > (d_2)(r_1):

Is (d_1)(r_2) > (d_2)(30 + r_2) ?

We see that we still cannot answer the question. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

**Statements One and Two Together: **

Using the information from statements one and two we have the following equations:

1) d_1 = 30 + d_2

2) r_1 = 30 + r_2

Since d_1 = 30 + d_2 and since r_1 = 30 + r_2, we can substitute 30 + d_2 for d_1 and 30 + r_2 for r_1 in the inequality (d_1)(r_2) > (d_2)(r_1):

Is (30 + d_2)(r_2) > (d_2)(30 + r_2) ?

Is (30)(r_2) + (d_2)(r_2) > (30)(d_2) + (d_2)(r_2) ?

Is (30)(r_2) > (30)(d_2) ?

Is r_2 > d_2 ?

Since we cannot determine whether r_2 is greater than d_2, statements one and two together are not sufficient to answer the question.

**Answer:** E