Question

Anabel's horse runs 24 miles per hour. Jackie's horse runs 28 miles per hour. Both horses stand at the starting line of a straight 2-mile track, and Jackie's horse starts running 30 seconds after Anabel's. How many miles from the starting line does Jackie's horse catch up to Anabel's?

Answer 1

Jackie's horse will catch up to Anabel's horse at a distance of 2 miles + (28 miles per hour x Total Time).

Step-by-step explanation:

To find the distance from the starting line where Jackie's horse catches up to Anabel's horse, we can use the formula:

Distance = Speed x Time

First, let's find the time it takes for Jackie's horse to catch up to Anabel's horse. Since Jackie's horse starts running 30 seconds after Anabel's, Jackie's horse has a head start of 30 seconds.

The time it takes for Jackie's horse to catch up to Anabel's is the same as the time it takes for Anabel's horse to cover 2 miles at their respective speeds. To find this time, we can use the formula:
Time = Distance / Speed

For Anabel's horse:
Time = 2 miles / 24 miles per hour = 1/12 hours

For Jackie's horse:
Time = 2 miles / 28 miles per hour = 1/14 hours

Since Jackie's horse started running 30 seconds later, we add 1/14 hours to 30 seconds:

Total Time = (1/14 hours) + (30 seconds / 3600 seconds per hour)

Now, let's find how far Jackie's horse will be from the starting line when it catches up to Anabel's horse. We can use the formula:
Distance = Speed x Time

For Jackie's horse:
Distance = 28 miles per hour x Total Time

Therefore, Jackie's horse will catch up to Anabel's horse at a distance of 2 miles plus the distance calculated above.

Answer: Jackie's horse will catch up to Anabel's horse at a distance of 2 miles + (28 miles per hour x Total Time)

Answer 2

Distance = rate * time
Distance traveled by Jackie's horse d = 28t
Distance traveled by Anabel's horse d = 24t + 1/5

28t = 24t + 1/5 4t = 1/5 t = 1/20 The same distance is traveled in 1/20 hour
d = 28t d = 28(1/20) d = 1 2/5
1 2/5 miles = 1.4 miles