SOLUTION: The bear lake in idaho is 24 miles long. Suppose john starts cycling at one end at 20 mph and ramona starts at the other end at 16 mph. How long would it take them to meet? A. 3

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Question 898212: The bear lake in idaho is 24 miles long. Suppose john starts cycling at one end at 20 mph and ramona starts at the other end at 16 mph. How long would it take them to meet?
A. 30 mins
b. 35 mins
c. 40 mins
d. 45 mins
e. 50 mins?
thank you
Found 2 solutions by rfer, Theo:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
converging at 20+16=36mph
24/36=0.67 hrs
60*0.67=40 minutes

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the lake is 24 miles long.
john starts at one end and ramona starts at the other end.
john is traveling at 20 miles per hour.
ramona is traveling at 16 miles per hour.

let d be the distance that john travels.
let 24 - d be the distance that ramona travels.

they will both travel a total of 24 miles because d + 24 - d = 20.

let t be the time that each travels.

they will both have traveled the same amount of time when they meet.

the formula is rate * time = distance.

for john, that will be 20 * t = d

for ramona, that will be 16 * t = 24 - d

you have 2 equations that need to be solved simultaneously,.

since d = 20 * t from the first equation, you can replace d with 20 * t in the second equation to get:

16 * t = 24 - (20 * t)

now you can solve for t.

simplify to get:

16 * t = 24 - 20* t

add 20*t to both sides of the equation to get:

36 * t = 24

divide both sides of the equation by 36 to get:

t = 24/36 = 2/3 of an hour.

they will meet in 2/3 of an hour.

rate * time = d

john will have traveled 20 * 2/3 = 40/3 miles.

ramona will have traveled 16 * 2/3 = 32/3 miles.

together they will have traveled 40/3 + 32/3 = 72/3 = 24 miles.

looks good.

time = 2/3 of an hour.

2/3 of an hours is equal to 2/3 * 60 = 120 / 3 minutes which is equal to 40 minutes.

that would be selection c.