Problem Variable Chart:

Ellen :

D =distance

Re =12 mi/hr T

Te = T

Kate

D =distance

Rk = 9 mi/hr

Tk = (T+15min)

Convert everything to same terms. Since time is in minutes, you have to convert the rates into miles/minute.

Ellen 12 miles/hr x 1 hr/ 60 min = 12/60 mi/min=

0.2 miles/min

Kate 9 miles/hr x 1 hr/60 min = 9/60 mi/min =

0.15 miles/min

So,

D= 0.2 mi/min x T , and

D= 0.15 mi/min x T + 15 min.

Set them equal to one another(I will drop the labels)

0.2 T = 0.15 ( T + 15 )

0.2T = 0.15T + (0.15)(15)

0.2 T = 0.15 T + 2.25

-0.15 T -0.15T

—————————————

0.05 T = 2.25

——- ——

0.05 0.05

T = 45 min. so go back to chart to see whose time is equal to T and it was Ellen.

a. 45 min.

b. 3:45 p.m.

You should now be able to do the second problem. Just draw the problem out with the airport in the middle . Draw one arrow going one way for airplane #1 and one for airplane #2. Assign an algabraic phrase to each airplane for distance, rate, and time using the information in the problem.

Then put a mark at the end of each of your lines and that is where each plane was at the end of the 2 hrs. Now from the problem you know that distance of plane 1 from the airport plus distance of plane 2 from the airport is equal to 1100 mi. Write that algabraic equation and solve for speed. Then plug your value for the speed into the equations and plug and chug to get the answers.