# Story problems

#### Jaybug11

##### New member
The problem is a herd of elephants is migrating. They are moving at a rate of 6 miles per hour. One elephant stood still and was left behind. The stray sensed danger and began running at a rate of 10 miles per hour to reach the herd. The stray caught up in 5 minutes.

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

#### mmm4444bot

##### Super Moderator
Staff member

Part (1) simply asks for the given time (in minutes) to be converted from minutes to hours.

There are 60 minutes in 1 hour; therefore, every minute is 1/60th of an hour.

1 min = 1/60 hr
2 min = 2/60 hr
3 min = 3/60 hr
et cetera

Of course, it is best to reduce any fractions to lowest terms, before usage in the famous formula which represents the following fact.

Any linear distance-traveled can be written as this product: rate-of-travel TIMES elapsed time

d = r * t

So, you know the value of r (the running rate of the stray elephant) because it's given.

You know the elapsed time (the value of t) because that's your answer to part (1).

Since you converted the time unit in the given t value to hours, you can now multiply r and t together, and the resulting product is the distance traveled (in miles).

d = r * t

The value that you get for d is the answer to part (2).

I welcome specific questions.

#### Jaybug11

##### New member
Now it wants to know how far the herd tracked while the elephant was standing still. How do you do that?

#### Denis

##### Senior Member
Jaybug11 said:
Now it wants to know how far the herd tracked while the elephant was standing still. How do you do that?
Who is "it" ? :shock:

#### mmm4444bot

##### Super Moderator
Staff member
Jaybug11 said:
how far the herd tracked while the elephant was standing still. How do you do that?

We use the same formula: d = rt
The herd moved some distance, and at that point in time the stray began running. Eventually, both the herd and the stray covered the same distance.

(time stray sat) + (time stray ran) = total herd time

Let the symbol T represent the number of hours that the stray sat and waited.

I mean, the elapsed time for the entire herd-trip is then T plus the answer to part (1), yes?

You have r for the herd because it's given.

d = r*t

You have d, the total distance for the herd-trip. That's the answer to part (2), yes?

Substitute your values for d and r and substitute your expression for t into the equation, and solve for T.

#### Jaybug11

##### New member
I'm still confused

Staff member