Nancy drives 20 miles to her school each day. If she drives 10 miles per hour faster, it takes her 4 minutes less to get to school. Find her new speed

Question

Solving word problems by rational equations

Answer 1

Hi Danny,

Let x be Nancy’s new speed. Then her old speed was x - 10.

The time it takes Nancy to get to school is found using the formula: time = distance / speed.

This means Nancy’s new time is 20 / x. Her old, slower time was 20 / (x - 10).

If we add 4 minutes (which is 4/60 or 1/15 of an hour) to her new time, we’d get her old time.

[20 / x] + [1/15] = [20 / (x-10)]

The least common denominator (LCD) of these three fractions is x * 15 * (x-10).

If we multiply the entire equation by the LCD, we get some canceling and end with:

[20 * 15 * (x-10)] + [x * (x-10)] = [20 * x * 15]

If we simplify each of the brackets by distributing the parentheses we get:

[300x - 3000] + [x² - 10x] = 300x

We can distribute the brackets:

300x - 3000 + x² - 10x = 300x

Subtract 300x from both sides:

x² -10x - 3000 = 0

Factor:

(x - 60)(x + 50) = 0

x = 60 or x = -50 but since speed is positive then x = 50 miles per hour is correct.

Please let me know if I can be more helpful, thanks!

Joe