Question

(will award medal!!) check my work??? To travel 60 miles, it takes sue, riding a Harley, 2 hours less time than it takes Matt to travel 50 miles riding a bicycle. Sue travels 10 miles per hour faster than Matt. Find the times and rates of Matt and sue.

Answer 1

ahh someone please help? I'm new to this site and this question is hard for me :/

Answer 2

I already have
SR= 60/ST
ST= MT-2
MR=50/MT
SR=MR+10

Answer 3

just want to know if I'm right!?

Answer 4

yes the equations are correct

Answer 5

use substitution to get equation with 1 variable....then work backwards to get other variables

Answer 6

wait so that's not the final answer?

Answer 7

--> 60/ST = MR + 10

--> 60/(MT -2) = MR +10

--> 60/(50/MR -2) = MR +10

Answer 8

whats that?

Answer 9

its using substitution to solve for MR

Answer 10

you have 4 variables and 4 equations

you have to solve the system

Answer 11

I'm confused... I didn't know I needed to solve for MR? i thought i just had to find the rates and times of "Matt and Sue" .. the questions doesnt ask me to solve?

Answer 12

its the same thing :)

you need numbers for how fast each are going and how long it takes them

Answer 13

oh okay... so if I'm using the subsitution method which one do I solve first?

Answer 14

doesn't matter....just get an equation with only 1 variable

Answer 15

like taking SR=MR+10
and making it 10(SR)=MR ??

Answer 16

idk if thats not right im really bad at this... whoever can just post all the work to solve this question and then explain it to help me understand it from there? I'm usually better at understanding if I can see the question and the work at the same time..

Answer 17

ok im not sure what you just did there ^^

have you solved a system of 2 equations before?

Answer 18

yes but a really long time ago..

Answer 19

im not really sure where to even start with this one

Answer 20

SR = MR + 10

--> 60/ST = MR + 10 (SR = 60/ST)

--> 60/(MT -2) = MR +10 (ST = MT-2)

--> 60/(50/MR -2) = MR +10 (MT = 50/MR)

does this make sense?

Answer 21

from here you can simplify and solve for MR

\[\frac{60}{\frac{50-2MR}{MR}} = MR +10\]
\[60MR = (MR +10)(50 -2MR)\]
\[2MR^2 + 30MR - 500 = 0\]
Factor
\[2(MR +25)(MR -10) = 0\]
MR must be positive
\[MR = 10\]

Answer 22

Ssue = 60/Tsue
Smatt = 50/Tmatt
Ssue = Smatt + 10
Tsue = Tmatt - 2

Substituting in some of the relationships to get everything in terms of Tmatt:

Smatt+10 = 60/(Tmatt - 2)
10 + 50/Tmatt = 60/(Tmatt-2)
(10 Tmatt + 50)/Tmatt = 60/(Tmatt-2)

(Tmatt-2)(10 Tmatt + 50) = 60 Tmatt
10 Tmatt^2 + 50 Tmatt - 20 Tmatt - 100 = 60 Tmatt
10 Tmatt^2 - 30 Tmatt - 100 = 0
Divide by 10 to make numbers smaller
Tmatt^2 - 3 Tmatt - 10 = 0
Solve by factoring or quadratic
Tmatt = -2, Tmatt = 5
Tmatt = 5 is the only solution that makes sense in the context of this problem.
From there you can find the others.