On a journey of 200km a motorist found out that if he were to increase his speed by 2km/h the journey will take 15 minutes less calculate his average speed

Answer 1

Let's say the motorist's average speed for the journey is "x" km/h.

If he were to increase his speed by 2 km/h, his new speed would be "x + 2" km/h.

The journey distance is 200 km.

We'll first calculate the time taken for the journey at the average speed "x" km/h.

Time taken = Distance / Speed
= 200 km / x km/h
= 200 / x hours

Next, we'll calculate the time taken for the journey at the increased speed of "x + 2" km/h.

Time taken at increased speed = Distance / Speed
= 200 km / (x + 2) km/h
= 200 / (x + 2) hours

According to the problem, the journey will take 15 minutes less if the motorist increases his speed by 2 km/h. Since there are 60 minutes in an hour, 15 minutes is equal to 15/60 = 1/4 of an hour.

So, the difference in time taken for the journey at both speeds is 1/4 hour.

\(\frac{200}{x} - \frac{200}{x+2} = \frac{1}{4}\)

To simplify the equation, let's multiply through by 4(x)(x+2) to get rid of the fractions:

800(x+2) - 800x = x(x+2)

800x + 1600 - 800x = x² + 2x

1600 = x² + 2x

Rearranging the equation:

x² + 2x - 1600 = 0

Now, let's solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = 2, and c = -1600.

x = (-2 ± √((2)² - 4(1)(-1600))) / (2 * 1)
x = (-2 ± √(4 + 6400)) / 2
x = (-2 ± √(6404)) / 2
x = (-2 ± 80.02) / 2

Ignoring the negative value (as average speed cannot be negative), we have:

x = (80.02 - 2) / 2
x = 78.02 / 2
x = 39.01 km/h

Therefore, the motorist's average speed for the journey is approximately 39.01 km/h.