ok plz help with this math problem!?

Question

ok first keep in mind that i am only in 7th grade algebra honors:
a migrating elephant herd started moving at a rate of 6 mph. one elephant stood still and was left behind. then this stray sensed danger and began to run at a rate of 10 mph to reach the herd. the stray caught up in 5min.
1:how long (in hours) did the stray run to catch up? how far did it run?
2:find the distance that the herd traveled while the stray ran to catch up. then write an expression for the total distance the herd traveled. let "x" represent the distance (in miles) that the herd traveled while the stray stood still.
3: use the distances you found in 1 and 2. write and solve an equation to find how far the herd traveled while the stray stood still.

ok remember i am only in 7th grade honors algebra, so please make it so that i understand what you put down.

oh and to the ppl who are just using calculators, the answer would be wrong because it is rounded, plus they are fractions

Answer 1

1. 5/60 or 1/12 represents the time in hours that the elephant traveled.
The elephant ran at 10 miles per hour for 5 minutes.
10 miles/ hour * 5/60 = 5/6 miles or .8333 miles

2. 6 miles per hour * (5/60 hours) = 0.5 miles

6 miles per hour (the time before the first elephant figured out he was alone)

distance = speed * time (let's call time, t)
x= 6 * (t)

3. 0.8333333 - 0.5 miles = .33333
a third of a mile

Answer 2

1. How many minutes are in an hour? 60.
So the elephant ran for 5/60 (1/12) of an hour.

How far did the elephant run?
Distance = Rate * Time

D = 10MPH *1/12 Hrs = 10/12 of an hour reduce to 5/6.

2. How far did the rest of the herd go while the stray was catching up?

6 MPH for 1/12 Hrs
6 * 1/12 = 6/12 mile reduce to 3/6 Mile

3. How far had the herd travelled before the stray started?

Subtract the answer from (1) and (2)
5/6 Miles (total distance) minus 3/6 miles (the distance the herd travelled while the stray caught up) = 2/6 or 1/3 of a mile.

Edited to use fractions instead of decimals per the asker.

Answer 3

1a) How long in hours did the stray run to catch up?
Just convert 5 minutes into hours (e.g. 5/60 hours or 1/12 hour)

1b) How far did it run?
It ran at 10 mph for 1/12 hour
Distance = Rate x Time
Distance = 10 x 1/12
Distance = 10/12
Distance = 5/6 mile

2a) Find the distance that the herd traveled while the stray ran to catch up.
The time is still 1/12 hour, but the rate of the herd is 6 mph.
Distance = Rate x Time.
Distance = 6 x 1/12
Distance = 6/12
Distance = 1/2 mile

2b) Write an expression for the total distance the herd traveled. let "x" represent the distance (in miles) that the herd traveled while the stray stood still.
Herd travelled for x miles before the the stray started running, then ran for another 1/2 mile. So an expression for the total distance would simply be:
x + 1/2

3) Use the distances you found in 1 and 2. write and solve an equation to find how far the herd traveled while the stray stood still.
The herd's distance = x + 1/2
The stray's distance = 5/6
But this is the same distance, so equate them:
x + 1/2 = 5/6

Now solve for x:
x = 5/6 - 1/2
x = 5/6 - 3/6
x = (5-3) / 6
x = 2/6
x = 1/3

So the herd travelled 1/3 mile while the stray stood still.

Answer 4

1. 1/12 of an hour
2. Herd travelled .2 miles