Allison drove home at 64 mph, but her brother Austin, who left at the same time, could drive at only 50 mph. When Allison arrived, Austin still had 70 miles to go. How far did Allison drive?

Question

Allison drove home at 64 mph, but her brother Austin, who left at the same time, could drive at only 50 mph. When Allison arrived, Austin still had 70 miles to go. How far did Allison drive?

Answer 1

Allison drove home at 64 mph, but her brother Austin, who left at the same time, could drive at only 50 mph. When Allison arrived, Austin still had 70 miles to go. How far did Allison drive?

This is a classic Rate * Times = Distance.....R x T = D...

Take the facts from the word problem and convert to a math EQUATION......SO

Allison_Rate = 64 MPH Austin_Rate = 50 MPH Time (T) = The same for both....so

Allison_Rate x T = Allison_Distance

Austin_Rate x T = Allison_Distance - 70

......We now have two equations and two unknowns......put the numbers into the equation we have...

64 T = D

50 T = D - 70 .....Do you see the two equations....and the two unknowns....T and D....

50 T = 64 T - 70 ....sub the first equation into the second..

14 T = 70

T= 70/14 = 5 hours D = 64 MPH x 5 hours = 320 Miles

check

64T = D ...... 64 (5) = 320 Miles.....the distance that Allison Drove

50 (5) = D - 70...... 250 = 320 - 70 = 250....that checks....

Answer 2

WHOPES PUT THT IN THE WRONG SPOT.....WE SHALL DO A VIDEO! because the tables I created do not turn out so well when pasted here:)

A few general hints to get you started:

1. Use the formulate r x t = distance

r = rate

t= time

d = distance

2. I would create a chart /table for each person (see "Table A"below) and fill in the known values for each variable which you know into the chart/table. It may also help to draw a picture!

3. Next we need to define our variables and place the known variables in the appropriate spot in our chart (refer to Table A and B to see what I mean).

A) Here is the "starter Chart:

Alison         Rate(mph)   x    Time (hrs)       = Distance (miles)

             |       64mph                       t        

-------------------------------------------------------------

Austin  |   Rate     x  Time                               = Distance

                    50mph                           t

---------------------------------------------------------

define variables:

r = rate = Speed in mph

t= time = we do not have a value for time so we will leave it as “t”

d= we do not have a specific distance for time but what we do know is there is a known relationship between how much further ahead Allison was from Austin

 Whatever the distance is Allison was 70 miles ahead of Austin. Thus, no matter what, we do know is the following (Refer to Table A and B to see how this fits with the Tables).

1)     whatever the distance (d) from the start (point a) to the final destination (point b), we know that Allisson has currently traveled the entire distance (d) or d miles between the two points.

2)     When Allison traveled the entire distance of “d miles Austin still had 70 miles left to complete the entire distance (d) from point a to b.

                         Now let’s start translating the above logical statements about (1-2)  into “math language.:

1)     

                 d = distance = 1) the total distance in miles from point a (start) to point b (finish/destination point.  

                   d = distance = 2) Also Allison’s current distance from the start.  They are the same thing correct?

                          Thus, we can then go ahead and put the variable “d” in or table in the slot for Allison.

2)     Now let’s describe Austin’s current distance in relationship to total distance from a to b or as we said this is also equal to Allison’s current distance.

Austin is 70 miles away from Allisson or is 70 miles from completing the entire distance “d”.

Thus we can say his current distance can be expressed as  d- 70 miles. We write this in the space below.

                         Alison         Rate(mph)   x    Time (hrs)       = Distance (miles)

                                           |       64mph                       t                 d

                  -------------------------------------------------------------

                       Austin  |   Rate     x  Time                               = Distance (miles)

                                                     50mph                           t           d-70

---------------------------------------------------------

Now that you have completed the chart we just need to set up a system of equations and solve for d to get Allison’s distance.

I will stop here for now….let me know if you need additional help, I may finish this with a video.