Question

0) Mr. Allen and Mrs. Benson start at the same time from two locations 288 mile

apart. They drive towards each other. Mr. Allen travels eight miles an hour
faster than Mrs. Benson. At the end of six hours they meet. What is the rate of
each?

Answer 1

Mrs. Benson - 20 mph and Mr. Allen - 28 mph.

Explanation:

Let's define Mrs. Benson's speed as "r" miles per hour. And, Mr. Allen drives 8 mph faster, so his speed is "r +8" mph.

When they meet in 6 hours, the total distance they have traveled will be 288 miles (since they started with a difference of 288 miles).

Distance = Speed × Time

For Mrs. Benson:

Distance = r × 6

For Mr. Allen:

Distance = (r + 8) × 6

Since they met when their distance was 288 miles:

r × 6 + (r + 8) × 6 = 288

Simplify the equation:

6r + 6(r + 8) = 288

6r + 6r + 48 = 288

12r + 48 = 288

Now take away 48 from both sides:

12r = 240

Finally, divide by 12:

r = 20

So, Mrs. Benson's speed is 20 mph, and Mr. Allen's speed is 20 + 8 = 28 mph.