distance and time word problem

**vance** · February 10th 2009, 04:59 PM

A man walks for 45 minutes at a rate of 3 mph, then jogs for 75 minutes at a rate of 5 mph, then sits and rests for 30 minutes, and finally walks for 1 hour and half.Find the rule of the function that expresses this distance traveled as a function of time [ Caution: Don't mix up the units of time ; use either minutes or hours , not both]

could someone help me with this problem? I sketched the graph ,and the ranges I got are from 0 to .75 , .75 to 2, 2 to 2.5 and 2.5 to 4 . I know that the first function is 3t and the third one is 6.25.However, I don't know how to write the other two ones.

Thanks in advance.

**mollymcf2009** · February 10th 2009, 06:28 PM

Originally Posted by vance

A man walks for 45 minutes at a rate of 3 mph, then jogs for 75 minutes at a rate of 5 mph, then sits and rests for 30 minutes, and finally walks for 1 hour and half.Find the rule of the function that expresses this distance traveled as a function of time [ Caution: Don't mix up the units of time ; use either minutes or hours , not both]

could someone help me with this problem? I sketched the graph ,and the ranges I got are from 0 to .75 , .75 to 2, 2 to 2.5 and 2.5 to 4 . I know that the first rule is 3t and the third one is 6.25.However, I don't know how to write the other two ones.

Thanks in advance.

Hello!

The function rule for this problem is
distance = rate x time
d = rt
To write the rule as the distance traveled as a function of the time it took to travel that distance you will need to evaluate each set of data using this function. Since you have 3 different rates of speed, and 4 time periods, you will have to calculate each one.

I changed the times to hours.

RATE TIME
0 $\rightarrow$ .5
3 $\rightarrow$ .75
5 $\rightarrow$ 1.25
3 $\rightarrow$ 1.5

So, distance as a function of time:
d= rt

1) $d(t) = 0t$ so $d(.5) = (0)(.5) = 0 miles$
2) $d(t) = 3t$ so $d(.75) = (3)(.75) = 2.25 miles$
3) $d(t) = 5(t)$ so $d(1.25) = (5)(1.25) = 6.25 miles$
4) $d(t) = 3t$ so $d(1.5) = (3)(1.5) = 4.5 miles$

Hope this is what you needed! Good luck!

**Soroban** · February 10th 2009, 07:05 PM

Hello, vance!

This is a tricky one!
Luckily, I've done one of these before . . .

A man walks for 45 minutes at a rate of 3 mph, then jogs for 75 minutes at 5 mph,
then sits and rests for 30 minutes, and finally walks for 1 hour and half.
Find the rule of the function that expresses this distance traveled as a function of time.

This is a piece-wise function.

The distance function depends on what time period is involved.

From $t=0\text{ to }t = 0.75$ , the distance function is: . $3t$
. . By the end of the 45 minutes, he has gone 2.25 miles.

From $t = 0.75\text{ to } t = 2$ , the distance function is: . $2.25 + 5t$
. . By the end of the 75 minutes, he has gone another 6.25 miles, a total of 8.5 miles.

From $t = 2\text{ to }t = 2.5$ , the distance function is: . $8.5 + 0t \:=\:8.5$
. . By the end of the 30 minutes, he hasn't moved; his total is still 8.5 miles.

From $t = 2.5\text{ to }4$ , the distance function is: . $8.5+3t$
. . By the end of the 90 minutes, he has gone another 4.5 miles, a total of 13 miles.

The function would be written like this:

. . $d(t) \;=\;\begin{Bmatrix}3t & & 0 \leq t \leq 0.75 \\ 2.25 + 5t & & 0.75 \leq t < 2 \\ 8.5 & & 2 \leq t \leq 2.5 \\ 8.5+3t & & 2.5 < t < 4 \end{Bmatrix}$

The graph would look like this:

Code:

      |
      |                               *
      |                            *  :
      |                         *     :
      |                      *        :
      |               * * *           :
      |             * :   :           :
      |           *   :   :           :
      |         *     :   :           :
      |       *       :   :           :
      |     *         :   :           :
      |  *  :         :   :           :
  - - * - - + - - - - + - + - - - - - + - -
      |     ¾         2   2½          4
      |

**vance** · February 10th 2009, 08:03 PM

Originally Posted by Soroban

Hello, vance!

This is a tricky one!
Luckily, I've done one of these before . . .

This is a piece-wise function.

The distance function depends on what time period is involved.

From $t=0\text{ to }t = 0.75$ , the distance function is: . $3t$
. . By the end of the 45 minutes, he has gone 2.25 miles.

From $t = 0.75\text{ to } t = 2$ , the distance function is: . $2.25 + 5t$
. . By the end of the 75 minutes, he has gone another 6.25 miles, a total of 8.5 miles.

From $t = 2\text{ to }t = 2.5$ , the distance function is: . $8.5 + 0t \:=\:8.5$
. . By the end of the 30 minutes, he hasn't moved; his total is still 8.5 miles.

From $t = 2.5\text{ to }4$ , the distance function is: . $8.5+3t$
. . By the end of the 90 minutes, he has gone another 4.5 miles, a total of 13 miles.

The function would be written like this:

. . $d(t) \;=\;\begin{Bmatrix}3t & & 0 \leq t \leq 0.75 \\ 2.25 + 5t & & 0.75 \leq t < 2 \\ 8.5 & & 2 \leq t \leq 2.5 \\ 8.5+3t & & 2.5 < t < 4 \end{Bmatrix}$

The graph would look like this:

Code:

      |
      |                               *
      |                            *  :
      |                         *     :
      |                      *        :
      |               * * *           :
      |             * :   :           :
      |           *   :   :           :
      |         *     :   :           :
      |       *       :   :           :
      |     *         :   :           :
      |  *  :         :   :           :
  - - * - - + - - - - + - + - - - - - + - -
      |     ¾         2   2½          4
      |

Thanks soroban. This is what I was looking for!!!

Thread: distance and time word problem

LinkBack

Thread Tools

Display

distance and time word problem

Similar Math Help Forum Discussions

Distance Time word problem

Distance Rate Time Word Problem

Speed Time Distance Word Problem

word problem using d=rt (distance = rate x time)

grade 10 word problems (speed, time, distance)

Search Tags