Wo cyclists, 72 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?

a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable

r

to represent the speed of the slower cyclist.

The faster cyclist is 12 m/h

The slower cyclist is 6 m/h

4r + 8r = 72miles

Step-by-step explanation:

The speed of the slower cyclist is r (mph)

The speed of the faster cyclist is 2*r (mph) because he is going 2 times faster than the slower cyclist. Now we know that both start at the same time and after 4 hours of riding they meet each other.

So the distance can be calculated by the next equation:

distance (miles) = velocity (mph) * time (hours)

Slower cyclist:

To get the Distance of the slower cyclist we have to substitute the information we have:

distance = r * 4 hours

distance = 4r

Faster cyclist:

To get the Distance of the faster cyclist we have to substitute the information of the faster cyclist in the equation:

distance = 2r * 4 hours

distance = 8r

Now we know that adding the distance of both cyclists will be 72 miles because that is when both meet after the 4 hours.

So we have the equation:

(distance of the slower cyclist) + (distance of the faster cyclist) = 72

If we substitute:

4r + 8r = 72miles

if we solve by adding:

12r = 72 miles

Now we just have to leave the r alone so we send the 12 to the other side to divide:

r = 72/12

r = 6 m/h this is the speed of the slower cyclist,

To get the speed of the faster cyclist we will have to multiply the speed of the slower time 2 because he is going 2 times faster.

2r = speed of the faster cyclist

2 * (6) = 12m/h

the faster cyclist was going 18 mph

the slower cyclist was going 9 mph

Step-by-step explanation:

72 : 4 = 18

18 : 2 = 9