Answer:
<u>Benjamin's rate in mph was 6.44</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
- Rate or speed of Adam = 6 mph
- Ten minutes later, Benjamin started to run from city B towards city A
- Simultaneously, Caroline started to bicycle at a rate of 11 mph from city A towards city B
2. If Caroline caught up to Benjamin 50 minutes after passing Adam, what was Benjamin's rate in mph?
A. Let's calculate when Caroline caught up Adam:
Adam's rate = 6 mph
Caroline's rate = 11 mph
10 minutes = 1/6 of an hour
Distance covered by Adam when Caroline started to bike = 6 * 1/6 = 1 mile
t = Time it took Caroline to catch up to Adam
Therefore, we can solve for t, this way:
11t = 6t + 1
11t - 6t = 1
5t = 1
t = 1/5 of an hour
t = 12 minutes
Caroline passed Adam after biking 12 minutes, therefore she caught up to Benjamin 50 minutes later, or after 62 minutes.
B. Let's calculate the distance she covered after 62 minutes, this way:
62 minutes = 1 hour and 2 minutes or 1 2/60 or 1.03
Distance covered by Caroline = Time * rate
Replacing with the values we have:
Distance covered by Caroline = 1 2/60 * 11
Distance covered by Caroline = 11 11/30 or 11.37 miles
Let's recall the distance from city A to city B is 18 miles, therefore Benjamin covered 6.63 miles (18 - 11.37) when Caroline caught up to him
C. Finally let's calculate Benjamin's rate, this way:
Rate = Distance/Time
Replacing with the values we know:
Rate = 6.63/1.03
<u>Rate = 6.44 mph (rounding to the next hundredth)</u>
