Determining equations for distance and rate formulas.

Question

Two cyclists leave towns 90 miles apart at the same time and travel towards each other. One cyclist travels 5 miles slower than the other. If they meet in 2 hours, what is the rate of each cyclist?

Answer 1

Let S= speed of Slow cyclist.l The fast cyclist , F travels at S+6. The rate of closure between the two is Rate=(2S+6) Distance is Velocitiy*Time. Distance is 180 and time is 5 hours.

soooo, 5*(2S+6)= 180 Expanding we get 10S+30 = 180 or 10S=150 or S=15. The slow rider pedals at 15 MPH and The faster at 21 mph. To check our work we see the low rider covers 15MPH*5hours = 75 miles. The other rider covers 21*5 = 105 miles. Between the two of them they cover the whole 180 miles.

Answer 2

The distance equation is as follows.

Distance = rate x time

To logically understand the equation, think about the units. We will be using miles and miles per hour and hours as the distance, rate, and time.

Miles = (miles/hour) x hour

Notice how the units on the right hand side will cancel out to leave the miles. it is important to use this when thinking about these equations.

For the equation above, we will let x be the rate of one cyclist. Their rates are 2x, to symbolize the 2 hours it takes to meet, and 2(x-5), to symbolize the slower cyclist. We will add these to form the total distance, 90 miles. The addition of these two rates equals the distance traveled, 90. This can be summed up in the equation:

2x + 2(x-5) = 90

2x + 2x-10 = 90

4x = 100

x = 25

The rate of the faster cyclist is 25 mph.

The rate of the slower cyclist is 20 mph.