Question

To travel 105 miles, it takes Sue, riding a moped, 3 hours less time than it takes Doreen to travel 64 miles riding a bicycle. Sue travels 13 miles per hour faster than Doreen. Find the times and rates of both girls.

Answer 1

Let t=time Doreen travels; let r=rate of Doreen
RATE * TIME = DIST.
Sue | r+13 t-3 105
Doreen | r t 64

Now solve the system:

(r+13)(t-3)=105
r*t=64

Answer 2

i still dont get the answer

Answer 3

i'm working the solution out now; lets see what i get

Answer 4

alright

Answer 5

This is what I got:
Doreen t=8 hr; r=8 mph
Sue's time=8-3=5 hr; Sues's rate=8+13=21 mph

Answer 6

that is all correct thank you

Answer 7

To solve the system, solve the second equation for r (or t, but I used r) and sub it into the first equation. It would look like this\[\left( \frac{64}{t}+13 \right)(t-3)=105\](do you want to see the steps to solve...)

Answer 8

yes that would be helpful

Answer 9

ok, from the lag line in my last post, I multiplied both side by t to clear the denominator\[64+13t)(t-3)=105t\]multiply and set equal to 0\[64t-192+13t^2-39t-105t=0\]\[13t^2-80t-192=0\]factor and solve (negative answer does not make sense)\[t=8 \cup t=-\frac{24}{13}\]to get Doreen's rate use r=64/t; to get Sues's info use the conversions in the table above.

Answer 10

"lag" is supposed to be "alg" meaning algebraic