1.) Claudia and her cousin Brian often ride their

bikes to meet each other. They live 16 miles

apart. Claudia can bike at a speed of 8.5 mph,

and Brian can ride 11mph. If they leave their

homes at the same time and bike toward each

other for half an hour, will they meet?

Answer: They do not meet.

Step-by-step explanation:

The distance between Claudia's house and her cousin Brian's house is 16 miles.

Claudia's speed is 8.5 miles per hour.

Brian's speed is 11 miles per hour.

If the part from their houses and travel for 0.5 hours, we have that the distance traveled by Claudia is equal to her velocity times the time she is biking, this is:

C = 8.5*0.5 = 4.25 miles.

So Claudia moves 4.25 miles towards Brian's house in this time, this means that Brian needs to move 16 miles - 4.25 miles = 11.75 miles.

Now, the distance that Brian moves is equal to his velocity times the time:

B = 11*0.5 = 5.5 miles

This is smaller than 11.75 miles, so they do not meet if they only bike for half an hour.

No, they will not meet.

Step-by-step explanation:

For them to meet, their combined distance covered must be equal to or greater than 16 miles

Given;

Claudia can bike at a speed of 8.5 mph

and Brian can ride 11mph

Time = 0.5 hour

Distance = speed * time

Total distance covered by both is;

d = (8.5+11) * 0.5 = 9.75miles

Since, the combined distance is less than 16.

d = 9.75 < 16

They will not meet.