Question

Paloma Rey drove to work on Wednesday at 40 miles per hour and

arrived one minute late. She left home at the same time on Thursday,
drove 45 miles per hour, and arrived one minute early. How far does
Ms. Rey drive to work?

Answer 1

Ms. Rey drives 1.5 miles to work.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations using the formula distance = rate x time.

Let's assume the distance Ms. Rey drives to work is d miles.

On Wednesday, she drove at a rate of 40 miles per hour and arrived one minute late. This means that she spent t1 hours driving. We can calculate t1 by converting 1 minute to hours: t1 = 1 minute / 60 minutes per hour = 1/60 hours. Therefore, using the formula, we have d = 40 * t1.

On Thursday, she drove at a rate of 45 miles per hour and arrived one minute early. This means that she spent t2 hours driving. We can calculate t2 by converting 1 minute to hours: t2 = 1 minute / 60 minutes per hour = 1/60 hours. Therefore, using the formula, we have d = 45 * t2.

Since both equations are equal to d, we can equate them: 40 * t1 = 45 * t2.

Now we can solve for t1:

t1 = (45 * t2) / 40.

Substituting the value of t2 in terms of t1:

t1 = (45 * (1/60)) / 40 = 45/2400 = 3/160.

Finally, we can use the formula distance = rate x time to find the distance Ms. Rey drives to work:

d = 40 * (3/160) = 6/4 = 1.5 miles.