Question

A driver of a car took a day trip around the coastline driving at two different speeds. He drove 90 miles at a slower speed and ​300 miles at a speed 30 miles per hour faster. If the time spent twice driving at the faster speed was twice that spent driving at the slower​ speed, find the two speeds during the trip.

Answer 1

Okay, let's see where this goes...
Answer:

A is smaller than B, we know

Explanation:

Let A represent the slower speed and B represent the faster speed.

First we need to find the total time spent driving.

Time spent driving at A: 90 miles / A miles per hour = 90/A hours

Time spent driving at B: 300 miles / B miles per hour = 300/B hours

Now we know how much time is spent driving at each speed.

But we still need to find how long each speed takes the driver.

So distance = speed x time, right?

So to find how long the trip takes using the slower speed, we'll use the equation:

Distance / Speed = Time

90 / A = Time

Now we can do the same to find how long it takes to drive 300 miles using the faster speed:

300 / B = Time

Now that we have both values for time, we can now compare them:

Time (faster speed) = 2 x Time (slower speed)

So now we can find all the values.

If 90 / A = Time and 300 / B = Time

Then we can solve to get:

A = Time x 90

B = Time x 300

So to determine which speed is slower and which speed is faster, we must compare the two times.

If A is the slower speed, then A is smaller than B. So let's see...

A = 90 x Time

B = 300 x Time

Since A is smaller than B, we know