I need help with a word problem

Question

A migrating elephant herd started moving at a rate of 6 miles per hour. One elephant stood still and was left behind. Then this stray elephant sensed danger and began running at a rate of 10 miles per hour to reach the herd. The stray caught up in 5 minutes.

 

 

How long (in hours) did the stray run to catch up? How far did it run?

 

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 elephant stood still.

 

 

 

Use the distances you found in Exercises 18 and 19. Write and solve an equation to find how far the herd traveled while the stray stood still.

Answer 1

Rech,

 

First we need to figure out what we know.  We know that the herd is traveling at six miles per hour. If it took 5 minutes for the stray to catch up they would have traveled 6(5/60) miles or 1/2 mile. The total distance the herd traveled is also the distance the stray traveled to catch up. The expression for total distance=stray miles per hour times (minutes to catch up/minutes in an hour) or total distance = 10(5/60) = 5/6 of a mile. 

The distance that herd traveled while the stray stood still would be the total distance minus the distance traveled by herd while the stray was catching up. The expression is x=(stray miles per hour times (minutes to catch up/minutes in an hour)) - (herd miles per hour times (minutes to catch up/minutes in an hour)) or x=(10(5/60))-(6(5/60))=5/6-1/2=1/3 mile.

 

Answer 2

Let's look at all of the questions:

 

First, the length of time in hours that the stray ran to catch up. We need to convert 5 minutes into hours:

 

5 min=(5 min)*((1 hr)/(60 min))

 

The minutes cancel and we have

 

(5/60) hr = (1/12) hr.

 

The distance it traveled is

 

speed*time = (10 miles/hr)*(1/12 hr)=10/12 miles = 5/6 miles.

 

While the stray was running to catch up, the herd was moving at 6 miles per hour. As we saw, the amount of time was 1/12 of an hour, so the distance the herd traveled during that time was

 

speed*time = (6 miles/hr)*(1/12 hr) = 1/2 mile.

 

Now we look at the total distance the herd traveled. It is the distance they traveled as the stray stood still -- which we denote x as per the problem statement -- plus the distance traveled while they stray was running -- which we just was was 1/2 mile. The expression is then

 

x+1/2

 

This is the distance traveled by the herd from the time the stray began standing still to the time the stray caught up. It is also therefore the distance that the stray covered in 1/12 hour running at 10 miles per hour. We have already calculated that distance at 5/6 miles, so we can set the expression equal to 5/6:

 

x+1/2=5/6.

 

Subtract 1/2 to solve for x:

 

x=5/6-1/2=1/3 miles.